In this project, you will apply unsupervised learning techniques to identify segments of the population that form the core customer base for a mail-order sales company in Germany. These segments can then be used to direct marketing campaigns towards audiences that will have the highest expected rate of returns. The data that you will use has been provided by our partners at Bertelsmann Arvato Analytics, and represents a real-life data science task.
This notebook will help you complete this task by providing a framework within which you will perform your analysis steps. In each step of the project, you will see some text describing the subtask that you will perform, followed by one or more code cells for you to complete your work. Feel free to add additional code and markdown cells as you go along so that you can explore everything in precise chunks. The code cells provided in the base template will outline only the major tasks, and will usually not be enough to cover all of the minor tasks that comprise it.
It should be noted that while there will be precise guidelines on how you should handle certain tasks in the project, there will also be places where an exact specification is not provided. There will be times in the project where you will need to make and justify your own decisions on how to treat the data. These are places where there may not be only one way to handle the data. In real-life tasks, there may be many valid ways to approach an analysis task. One of the most important things you can do is clearly document your approach so that other scientists can understand the decisions you've made.
At the end of most sections, there will be a Markdown cell labeled Discussion. In these cells, you will report your findings for the completed section, as well as document the decisions that you made in your approach to each subtask. Your project will be evaluated not just on the code used to complete the tasks outlined, but also your communication about your observations and conclusions at each stage.
# import libraries here; add more as necessary
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
# magic word for producing visualizations in notebook
%matplotlib inline
There are four files associated with this project (not including this one):
Udacity_AZDIAS_Subset.csv: Demographics data for the general population of Germany; 891211 persons (rows) x 85 features (columns).Udacity_CUSTOMERS_Subset.csv: Demographics data for customers of a mail-order company; 191652 persons (rows) x 85 features (columns).Data_Dictionary.md: Detailed information file about the features in the provided datasets.AZDIAS_Feature_Summary.csv: Summary of feature attributes for demographics data; 85 features (rows) x 4 columnsEach row of the demographics files represents a single person, but also includes information outside of individuals, including information about their household, building, and neighborhood. You will use this information to cluster the general population into groups with similar demographic properties. Then, you will see how the people in the customers dataset fit into those created clusters. The hope here is that certain clusters are over-represented in the customers data, as compared to the general population; those over-represented clusters will be assumed to be part of the core userbase. This information can then be used for further applications, such as targeting for a marketing campaign.
To start off with, load in the demographics data for the general population into a pandas DataFrame, and do the same for the feature attributes summary. Note for all of the .csv data files in this project: they're semicolon (;) delimited, so you'll need an additional argument in your read_csv() call to read in the data properly. Also, considering the size of the main dataset, it may take some time for it to load completely.
Once the dataset is loaded, it's recommended that you take a little bit of time just browsing the general structure of the dataset and feature summary file. You'll be getting deep into the innards of the cleaning in the first major step of the project, so gaining some general familiarity can help you get your bearings.
# Load in the general demographics data.
azdias = pd.read_csv("Udacity_AZDIAS_Subset.csv", sep=';')
# Load in the feature summary file.
feat_info = pd.read_csv("AZDIAS_Feature_Summary.csv", sep=';')
# Check the structure of the general demographic data after it's loaded (e.g. print the number of
# rows and columns, print the first few rows).
print(azdias.head())
print('Shape')
print(azdias.shape)
AGER_TYP ALTERSKATEGORIE_GROB ANREDE_KZ CJT_GESAMTTYP \ 0 -1 2 1 2.0 1 -1 1 2 5.0 2 -1 3 2 3.0 3 2 4 2 2.0 4 -1 3 1 5.0 FINANZ_MINIMALIST FINANZ_SPARER FINANZ_VORSORGER FINANZ_ANLEGER \ 0 3 4 3 5 1 1 5 2 5 2 1 4 1 2 3 4 2 5 2 4 4 3 4 1 FINANZ_UNAUFFAELLIGER FINANZ_HAUSBAUER ... PLZ8_ANTG1 PLZ8_ANTG2 \ 0 5 3 ... NaN NaN 1 4 5 ... 2.0 3.0 2 3 5 ... 3.0 3.0 3 1 2 ... 2.0 2.0 4 3 2 ... 2.0 4.0 PLZ8_ANTG3 PLZ8_ANTG4 PLZ8_BAUMAX PLZ8_HHZ PLZ8_GBZ ARBEIT \ 0 NaN NaN NaN NaN NaN NaN 1 2.0 1.0 1.0 5.0 4.0 3.0 2 1.0 0.0 1.0 4.0 4.0 3.0 3 2.0 0.0 1.0 3.0 4.0 2.0 4 2.0 1.0 2.0 3.0 3.0 4.0 ORTSGR_KLS9 RELAT_AB 0 NaN NaN 1 5.0 4.0 2 5.0 2.0 3 3.0 3.0 4 6.0 5.0 [5 rows x 85 columns] Shape (891221, 85)
azdias.describe()
| AGER_TYP | ALTERSKATEGORIE_GROB | ANREDE_KZ | CJT_GESAMTTYP | FINANZ_MINIMALIST | FINANZ_SPARER | FINANZ_VORSORGER | FINANZ_ANLEGER | FINANZ_UNAUFFAELLIGER | FINANZ_HAUSBAUER | ... | PLZ8_ANTG1 | PLZ8_ANTG2 | PLZ8_ANTG3 | PLZ8_ANTG4 | PLZ8_BAUMAX | PLZ8_HHZ | PLZ8_GBZ | ARBEIT | ORTSGR_KLS9 | RELAT_AB | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| count | 891221.000000 | 891221.000000 | 891221.000000 | 886367.000000 | 891221.000000 | 891221.000000 | 891221.000000 | 891221.000000 | 891221.000000 | 891221.000000 | ... | 774706.000000 | 774706.000000 | 774706.000000 | 774706.000000 | 774706.000000 | 774706.000000 | 774706.000000 | 794005.000000 | 794005.000000 | 794005.00000 |
| mean | -0.358435 | 2.777398 | 1.522098 | 3.632838 | 3.074528 | 2.821039 | 3.401106 | 3.033328 | 2.874167 | 3.075121 | ... | 2.253330 | 2.801858 | 1.595426 | 0.699166 | 1.943913 | 3.612821 | 3.381087 | 3.167854 | 5.293002 | 3.07222 |
| std | 1.198724 | 1.068775 | 0.499512 | 1.595021 | 1.321055 | 1.464749 | 1.322134 | 1.529603 | 1.486731 | 1.353248 | ... | 0.972008 | 0.920309 | 0.986736 | 0.727137 | 1.459654 | 0.973967 | 1.111598 | 1.002376 | 2.303739 | 1.36298 |
| min | -1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | ... | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 0.000000 | 1.00000 |
| 25% | -1.000000 | 2.000000 | 1.000000 | 2.000000 | 2.000000 | 1.000000 | 3.000000 | 2.000000 | 2.000000 | 2.000000 | ... | 1.000000 | 2.000000 | 1.000000 | 0.000000 | 1.000000 | 3.000000 | 3.000000 | 3.000000 | 4.000000 | 2.00000 |
| 50% | -1.000000 | 3.000000 | 2.000000 | 4.000000 | 3.000000 | 3.000000 | 3.000000 | 3.000000 | 3.000000 | 3.000000 | ... | 2.000000 | 3.000000 | 2.000000 | 1.000000 | 1.000000 | 4.000000 | 3.000000 | 3.000000 | 5.000000 | 3.00000 |
| 75% | -1.000000 | 4.000000 | 2.000000 | 5.000000 | 4.000000 | 4.000000 | 5.000000 | 5.000000 | 4.000000 | 4.000000 | ... | 3.000000 | 3.000000 | 2.000000 | 1.000000 | 3.000000 | 4.000000 | 4.000000 | 4.000000 | 7.000000 | 4.00000 |
| max | 3.000000 | 9.000000 | 2.000000 | 6.000000 | 5.000000 | 5.000000 | 5.000000 | 5.000000 | 5.000000 | 5.000000 | ... | 4.000000 | 4.000000 | 3.000000 | 2.000000 | 5.000000 | 5.000000 | 5.000000 | 9.000000 | 9.000000 | 9.00000 |
8 rows × 81 columns
# Check the structure of the feature summary data after it's loaded (e.g. print the number of
# rows and columns, print the first few rows).
print(feat_info.head())
print('Shape')
print(feat_info.shape)
attribute information_level type missing_or_unknown 0 AGER_TYP person categorical [-1,0] 1 ALTERSKATEGORIE_GROB person ordinal [-1,0,9] 2 ANREDE_KZ person categorical [-1,0] 3 CJT_GESAMTTYP person categorical [0] 4 FINANZ_MINIMALIST person ordinal [-1] Shape (85, 4)
feat_info_missing = feat_info[['attribute', 'missing_or_unknown']]
print(feat_info_missing.head())
attribute missing_or_unknown 0 AGER_TYP [-1,0] 1 ALTERSKATEGORIE_GROB [-1,0,9] 2 ANREDE_KZ [-1,0] 3 CJT_GESAMTTYP [0] 4 FINANZ_MINIMALIST [-1]
Tip: Add additional cells to keep everything in reasonably-sized chunks! Keyboard shortcut
esc --> a(press escape to enter command mode, then press the 'A' key) adds a new cell before the active cell, andesc --> badds a new cell after the active cell. If you need to convert an active cell to a markdown cell, useesc --> mand to convert to a code cell, useesc --> y.
The feature summary file contains a summary of properties for each demographics data column. You will use this file to help you make cleaning decisions during this stage of the project. First of all, you should assess the demographics data in terms of missing data. Pay attention to the following points as you perform your analysis, and take notes on what you observe. Make sure that you fill in the Discussion cell with your findings and decisions at the end of each step that has one!
The fourth column of the feature attributes summary (loaded in above as feat_info) documents the codes from the data dictionary that indicate missing or unknown data. While the file encodes this as a list (e.g. [-1,0]), this will get read in as a string object. You'll need to do a little bit of parsing to make use of it to identify and clean the data. Convert data that matches a 'missing' or 'unknown' value code into a numpy NaN value. You might want to see how much data takes on a 'missing' or 'unknown' code, and how much data is naturally missing, as a point of interest.
As one more reminder, you are encouraged to add additional cells to break up your analysis into manageable chunks.
print(azdias.shape[0] * .2)
178244.2
print(azdias.head())
AGER_TYP ALTERSKATEGORIE_GROB ANREDE_KZ CJT_GESAMTTYP \ 0 -1 2 1 2.0 1 -1 1 2 5.0 2 -1 3 2 3.0 3 2 4 2 2.0 4 -1 3 1 5.0 FINANZ_MINIMALIST FINANZ_SPARER FINANZ_VORSORGER FINANZ_ANLEGER \ 0 3 4 3 5 1 1 5 2 5 2 1 4 1 2 3 4 2 5 2 4 4 3 4 1 FINANZ_UNAUFFAELLIGER FINANZ_HAUSBAUER ... PLZ8_ANTG1 PLZ8_ANTG2 \ 0 5 3 ... NaN NaN 1 4 5 ... 2.0 3.0 2 3 5 ... 3.0 3.0 3 1 2 ... 2.0 2.0 4 3 2 ... 2.0 4.0 PLZ8_ANTG3 PLZ8_ANTG4 PLZ8_BAUMAX PLZ8_HHZ PLZ8_GBZ ARBEIT \ 0 NaN NaN NaN NaN NaN NaN 1 2.0 1.0 1.0 5.0 4.0 3.0 2 1.0 0.0 1.0 4.0 4.0 3.0 3 2.0 0.0 1.0 3.0 4.0 2.0 4 2.0 1.0 2.0 3.0 3.0 4.0 ORTSGR_KLS9 RELAT_AB 0 NaN NaN 1 5.0 4.0 2 5.0 2.0 3 3.0 3.0 4 6.0 5.0 [5 rows x 85 columns]
# Identify missing or unknown data values and convert them to NaNs.
print(feat_info_missing.loc[feat_info_missing['attribute'] == 'AGER_TYP'])
test1 = feat_info_missing.loc[feat_info_missing['attribute'] == 'ANREDE_KZ']
print(test1['missing_or_unknown'][2])
attribute missing_or_unknown 0 AGER_TYP [-1,0] [-1,0]
# find out the different kind of encodings
feat_info.missing_or_unknown.unique()
array(['[-1,0]', '[-1,0,9]', '[0]', '[-1]', '[]', '[-1,9]', '[-1,X]',
'[XX]', '[-1,XX]'], dtype=object)
def obtain_missing_info(test):
if('[-1,0]' == test):
return [-1,0]
if('[-1,0,9]' == test):
return [-1,0,9]
if('[0]' == test):
return [0]
if('[-1]' == test):
return [-1]
if('[-1,9]' == test):
return [-1,9]
if('[-1,X]' == test):
return [-1,'X']
if('[XX]' == test):
return ['XX']
if('[-1,XX]' == test):
return [-1,'XX']
counter = 0
for x in azdias.iteritems():
col_name = feat_info_missing.loc[feat_info_missing['attribute'] == x[0]]
missing = col_name['missing_or_unknown'][counter]
counter = counter + 1
if(len(missing) > 2):
azdias[x[0]] = azdias[x[0]].replace(obtain_missing_info(missing), np.NaN)
print(azdias[:20])
AGER_TYP ALTERSKATEGORIE_GROB ANREDE_KZ CJT_GESAMTTYP \
0 NaN 2.0 1 2.0
1 NaN 1.0 2 5.0
2 NaN 3.0 2 3.0
3 2.0 4.0 2 2.0
4 NaN 3.0 1 5.0
5 3.0 1.0 2 2.0
6 NaN 2.0 2 5.0
7 NaN 1.0 1 3.0
8 NaN 3.0 1 3.0
9 NaN 3.0 2 4.0
10 NaN 3.0 2 1.0
11 NaN 2.0 1 6.0
12 NaN 3.0 1 6.0
13 NaN 1.0 2 5.0
14 NaN 3.0 1 6.0
15 1.0 4.0 2 4.0
16 NaN 1.0 2 1.0
17 NaN 2.0 1 6.0
18 NaN 2.0 2 6.0
19 NaN 3.0 1 3.0
FINANZ_MINIMALIST FINANZ_SPARER FINANZ_VORSORGER FINANZ_ANLEGER \
0 3 4 3 5
1 1 5 2 5
2 1 4 1 2
3 4 2 5 2
4 4 3 4 1
5 3 1 5 2
6 1 5 1 5
7 3 3 4 1
8 4 4 2 4
9 2 4 2 3
10 2 2 5 3
11 3 4 3 5
12 5 3 4 2
13 1 4 3 5
14 3 4 3 5
15 4 1 5 1
16 4 3 1 4
17 3 4 3 5
18 2 4 1 5
19 5 2 3 1
FINANZ_UNAUFFAELLIGER FINANZ_HAUSBAUER ... PLZ8_ANTG1 PLZ8_ANTG2 \
0 5 3 ... NaN NaN
1 4 5 ... 2.0 3.0
2 3 5 ... 3.0 3.0
3 1 2 ... 2.0 2.0
4 3 2 ... 2.0 4.0
5 2 5 ... 2.0 3.0
6 4 3 ... 3.0 3.0
7 3 2 ... 3.0 3.0
8 2 2 ... 2.0 3.0
9 5 4 ... 2.0 3.0
10 1 5 ... 2.0 4.0
11 5 3 ... NaN NaN
12 4 1 ... 3.0 3.0
13 5 2 ... 2.0 1.0
14 5 3 ... NaN NaN
15 1 4 ... NaN NaN
16 5 1 ... 3.0 3.0
17 5 3 ... NaN NaN
18 4 1 ... 2.0 3.0
19 3 1 ... 2.0 4.0
PLZ8_ANTG3 PLZ8_ANTG4 PLZ8_BAUMAX PLZ8_HHZ PLZ8_GBZ ARBEIT \
0 NaN NaN NaN NaN NaN NaN
1 2.0 1.0 1.0 5.0 4.0 3.0
2 1.0 0.0 1.0 4.0 4.0 3.0
3 2.0 0.0 1.0 3.0 4.0 2.0
4 2.0 1.0 2.0 3.0 3.0 4.0
5 1.0 1.0 1.0 5.0 5.0 2.0
6 1.0 0.0 1.0 5.0 5.0 4.0
7 1.0 0.0 1.0 4.0 4.0 2.0
8 2.0 1.0 1.0 3.0 3.0 2.0
9 2.0 1.0 1.0 3.0 3.0 2.0
10 2.0 0.0 2.0 3.0 3.0 4.0
11 NaN NaN NaN NaN NaN NaN
12 1.0 0.0 1.0 5.0 5.0 3.0
13 1.0 1.0 1.0 3.0 3.0 3.0
14 NaN NaN NaN NaN NaN NaN
15 NaN NaN NaN NaN NaN 4.0
16 1.0 0.0 1.0 3.0 4.0 1.0
17 NaN NaN NaN NaN NaN NaN
18 2.0 1.0 1.0 3.0 3.0 3.0
19 2.0 1.0 2.0 5.0 4.0 4.0
ORTSGR_KLS9 RELAT_AB
0 NaN NaN
1 5.0 4.0
2 5.0 2.0
3 3.0 3.0
4 6.0 5.0
5 3.0 3.0
6 6.0 3.0
7 5.0 2.0
8 4.0 3.0
9 3.0 1.0
10 6.0 5.0
11 NaN NaN
12 6.0 4.0
13 6.0 4.0
14 NaN NaN
15 8.0 5.0
16 2.0 1.0
17 NaN NaN
18 4.0 3.0
19 6.0 3.0
[20 rows x 85 columns]
How much missing data is present in each column? There are a few columns that are outliers in terms of the proportion of values that are missing. You will want to use matplotlib's hist() function to visualize the distribution of missing value counts to find these columns. Identify and document these columns. While some of these columns might have justifications for keeping or re-encoding the data, for this project you should just remove them from the dataframe. (Feel free to make remarks about these outlier columns in the discussion, however!)
For the remaining features, are there any patterns in which columns have, or share, missing data?
# Perform an assessment of how much missing data there is in each column of the
# dataset.
column_dict = {}
for column in azdias:
counts = azdias[column].isnull().sum()
if(counts > 0):
column_dict[column] = counts
print(len(azdias.columns))
plt.figure(figsize=(20,6))
plt.bar(column_dict.keys(), column_dict.values())
plt.xlabel('columns')
plt.ylabel('Amount')
plt.show()
85
It appears that a majority have roughly 200K or below in terms of NaN.
I will be removing the outliers that have more than 200,000 in NAN
#Listed below are the names of the columns that have more than 200K NaN
print(azdias.keys())
Index(['AGER_TYP', 'ALTERSKATEGORIE_GROB', 'ANREDE_KZ', 'CJT_GESAMTTYP',
'FINANZ_MINIMALIST', 'FINANZ_SPARER', 'FINANZ_VORSORGER',
'FINANZ_ANLEGER', 'FINANZ_UNAUFFAELLIGER', 'FINANZ_HAUSBAUER',
'FINANZTYP', 'GEBURTSJAHR', 'GFK_URLAUBERTYP', 'GREEN_AVANTGARDE',
'HEALTH_TYP', 'LP_LEBENSPHASE_FEIN', 'LP_LEBENSPHASE_GROB',
'LP_FAMILIE_FEIN', 'LP_FAMILIE_GROB', 'LP_STATUS_FEIN',
'LP_STATUS_GROB', 'NATIONALITAET_KZ', 'PRAEGENDE_JUGENDJAHRE',
'RETOURTYP_BK_S', 'SEMIO_SOZ', 'SEMIO_FAM', 'SEMIO_REL', 'SEMIO_MAT',
'SEMIO_VERT', 'SEMIO_LUST', 'SEMIO_ERL', 'SEMIO_KULT', 'SEMIO_RAT',
'SEMIO_KRIT', 'SEMIO_DOM', 'SEMIO_KAEM', 'SEMIO_PFLICHT', 'SEMIO_TRADV',
'SHOPPER_TYP', 'SOHO_KZ', 'TITEL_KZ', 'VERS_TYP', 'ZABEOTYP',
'ALTER_HH', 'ANZ_PERSONEN', 'ANZ_TITEL', 'HH_EINKOMMEN_SCORE',
'KK_KUNDENTYP', 'W_KEIT_KIND_HH', 'WOHNDAUER_2008',
'ANZ_HAUSHALTE_AKTIV', 'ANZ_HH_TITEL', 'GEBAEUDETYP', 'KONSUMNAEHE',
'MIN_GEBAEUDEJAHR', 'OST_WEST_KZ', 'WOHNLAGE', 'CAMEO_DEUG_2015',
'CAMEO_DEU_2015', 'CAMEO_INTL_2015', 'KBA05_ANTG1', 'KBA05_ANTG2',
'KBA05_ANTG3', 'KBA05_ANTG4', 'KBA05_BAUMAX', 'KBA05_GBZ', 'BALLRAUM',
'EWDICHTE', 'INNENSTADT', 'GEBAEUDETYP_RASTER', 'KKK', 'MOBI_REGIO',
'ONLINE_AFFINITAET', 'REGIOTYP', 'KBA13_ANZAHL_PKW', 'PLZ8_ANTG1',
'PLZ8_ANTG2', 'PLZ8_ANTG3', 'PLZ8_ANTG4', 'PLZ8_BAUMAX', 'PLZ8_HHZ',
'PLZ8_GBZ', 'ARBEIT', 'ORTSGR_KLS9', 'RELAT_AB'],
dtype='object')
# Remove the outlier columns from the dataset. (You'll perform other data
# engineering tasks such as re-encoding and imputation later.)
for column in azdias:
counts = azdias[column].isnull().sum()
if(counts >= (azdias.shape[0] * .2)):
print(column)
azdias = azdias.drop(column, axis=1)
print(len(azdias.columns))
print(azdias.shape)
AGER_TYP GEBURTSJAHR TITEL_KZ ALTER_HH KK_KUNDENTYP KBA05_BAUMAX 79 (891221, 79)
There were two columns that were large outliers int eh dataset: 'AGER_TYP' and 'KK_KUNDENTYP'. I have dropped these from the dataframe
Now, you'll perform a similar assessment for the rows of the dataset. How much data is missing in each row? As with the columns, you should see some groups of points that have a very different numbers of missing values. Divide the data into two subsets: one for data points that are above some threshold for missing values, and a second subset for points below that threshold.
In order to know what to do with the outlier rows, we should see if the distribution of data values on columns that are not missing data (or are missing very little data) are similar or different between the two groups. Select at least five of these columns and compare the distribution of values.
countplot() function to create a bar chart of code frequencies and matplotlib's subplot() function to put bar charts for the two subplots side by side.Depending on what you observe in your comparison, this will have implications on how you approach your conclusions later in the analysis. If the distributions of non-missing features look similar between the data with many missing values and the data with few or no missing values, then we could argue that simply dropping those points from the analysis won't present a major issue. On the other hand, if the data with many missing values looks very different from the data with few or no missing values, then we should make a note on those data as special. Make sure you report your observations in the discussion section. Either way, you should continue your analysis below using just the subset of the data with few or no missing values.
# How much data is missing in each row of the dataset?
has_nulls = azdias.isnull().sum(axis=1)
plt.figure(figsize=(20,6))
ax = sns.countplot(has_nulls)
ax.set_xticklabels(ax.get_xticklabels(), rotation=40, ha="right")
plt.show()
# Write code to divide the data into two subsets based on the number of missing
# values in each row.
#Group_1 has the NA that has less than 15 N/A
group_1 = pd.DataFrame(columns=list(azdias))
#Group_2 has the NA that has more than 15 or more N/A
group_2 = pd.DataFrame(columns=list(azdias))
azdias = azdias.assign(Count_NA = lambda x: x.isnull().sum(axis=1)).sort_values('Count_NA', ascending=False).drop('Count_NA', axis=1)
print(azdias[103677:103678].isnull().sum().sum())
14
group_1 = azdias[103678:]
group_2 = azdias[0:103678]
print('Azdias shape')
print(azdias.shape)
print('Group 1 shape')
print(group_1.shape)
print('Group 2 shape')
print(group_2.shape)
Azdias shape (891221, 79) Group 1 shape (787543, 79) Group 2 shape (103678, 79)
print(group_2.head())
ALTERSKATEGORIE_GROB ANREDE_KZ CJT_GESAMTTYP FINANZ_MINIMALIST \
732775 3.0 2 NaN 3
643174 3.0 1 NaN 2
472919 1.0 1 NaN 5
345274 1.0 2 6.0 3
299868 2.0 2 6.0 3
FINANZ_SPARER FINANZ_VORSORGER FINANZ_ANLEGER \
732775 5 3 5
643174 5 3 5
472919 1 5 2
345274 4 3 5
299868 4 3 5
FINANZ_UNAUFFAELLIGER FINANZ_HAUSBAUER FINANZTYP ... \
732775 5 2 4 ...
643174 5 2 4 ...
472919 3 2 2 ...
345274 5 3 4 ...
299868 5 3 4 ...
PLZ8_ANTG1 PLZ8_ANTG2 PLZ8_ANTG3 PLZ8_ANTG4 PLZ8_BAUMAX PLZ8_HHZ \
732775 NaN NaN NaN NaN NaN NaN
643174 NaN NaN NaN NaN NaN NaN
472919 NaN NaN NaN NaN NaN NaN
345274 NaN NaN NaN NaN NaN NaN
299868 NaN NaN NaN NaN NaN NaN
PLZ8_GBZ ARBEIT ORTSGR_KLS9 RELAT_AB
732775 NaN NaN NaN NaN
643174 NaN NaN NaN NaN
472919 NaN NaN NaN NaN
345274 NaN NaN NaN NaN
299868 NaN NaN NaN NaN
[5 rows x 79 columns]
#Determining columns that have under 5K NaN
column_names = []
for column in azdias:
counts = azdias[column].isnull().sum()
if(counts < 5000):
column_names.append(column)
print(column)
print(counts)
ALTERSKATEGORIE_GROB 2881 ANREDE_KZ 0 CJT_GESAMTTYP 4854 FINANZ_MINIMALIST 0 FINANZ_SPARER 0 FINANZ_VORSORGER 0 FINANZ_ANLEGER 0 FINANZ_UNAUFFAELLIGER 0 FINANZ_HAUSBAUER 0 FINANZTYP 0 GFK_URLAUBERTYP 4854 GREEN_AVANTGARDE 0 LP_STATUS_FEIN 4854 LP_STATUS_GROB 4854 RETOURTYP_BK_S 4854 SEMIO_SOZ 0 SEMIO_FAM 0 SEMIO_REL 0 SEMIO_MAT 0 SEMIO_VERT 0 SEMIO_LUST 0 SEMIO_ERL 0 SEMIO_KULT 0 SEMIO_RAT 0 SEMIO_KRIT 0 SEMIO_DOM 0 SEMIO_KAEM 0 SEMIO_PFLICHT 0 SEMIO_TRADV 0 ZABEOTYP 0 ONLINE_AFFINITAET 4854
#Choosing the following 5 columns as they are under 5K in NaN
top_5_columns = ['CJT_GESAMTTYP', 'FINANZ_SPARER', 'GFK_URLAUBERTYP', 'LP_STATUS_FEIN', 'SEMIO_VERT']
# Compare the distribution of values for at least five columns where there are
# no or few missing values, between the two subsets.
plt.figure(figsize=(15,6))
plt.subplots_adjust(wspace=1, hspace=1)
def print_graphs(columns, data_group_1, data_group_2):
count = 1
for y in range(0,len(top_5_columns) - 1):
for z in range(1,3):
plt.subplot(5, 2, count)
count = count + 1
if(z == 1):
sns.countplot(x=azdias[columns[y]], data=data_group_1)
else:
sns.countplot(x=azdias[columns[y]], data=data_group_2)
plt.show()
print_graphs(top_5_columns, group_1, group_2)
#For the simplicity of this project, I am dropping rows of data
print(azdias.shape)
azdias = azdias.dropna(axis=0, inplace=False)
print(azdias.shape)
(891221, 79) (623209, 79)
Strangely enough, it does not look like there is a difference between the two
Checking for missing data isn't the only way in which you can prepare a dataset for analysis. Since the unsupervised learning techniques to be used will only work on data that is encoded numerically, you need to make a few encoding changes or additional assumptions to be able to make progress. In addition, while almost all of the values in the dataset are encoded using numbers, not all of them represent numeric values. Check the third column of the feature summary (feat_info) for a summary of types of measurement.
In the first two parts of this sub-step, you will perform an investigation of the categorical and mixed-type features and make a decision on each of them, whether you will keep, drop, or re-encode each. Then, in the last part, you will create a new data frame with only the selected and engineered columns.
Data wrangling is often the trickiest part of the data analysis process, and there's a lot of it to be done here. But stick with it: once you're done with this step, you'll be ready to get to the machine learning parts of the project!
print('Testing the feature_info column')
print(feat_info)
Testing the feature_info column
attribute information_level type missing_or_unknown
0 AGER_TYP person categorical [-1,0]
1 ALTERSKATEGORIE_GROB person ordinal [-1,0,9]
2 ANREDE_KZ person categorical [-1,0]
3 CJT_GESAMTTYP person categorical [0]
4 FINANZ_MINIMALIST person ordinal [-1]
5 FINANZ_SPARER person ordinal [-1]
6 FINANZ_VORSORGER person ordinal [-1]
7 FINANZ_ANLEGER person ordinal [-1]
8 FINANZ_UNAUFFAELLIGER person ordinal [-1]
9 FINANZ_HAUSBAUER person ordinal [-1]
10 FINANZTYP person categorical [-1]
11 GEBURTSJAHR person numeric [0]
12 GFK_URLAUBERTYP person categorical []
13 GREEN_AVANTGARDE person categorical []
14 HEALTH_TYP person ordinal [-1,0]
15 LP_LEBENSPHASE_FEIN person mixed [0]
16 LP_LEBENSPHASE_GROB person mixed [0]
17 LP_FAMILIE_FEIN person categorical [0]
18 LP_FAMILIE_GROB person categorical [0]
19 LP_STATUS_FEIN person categorical [0]
20 LP_STATUS_GROB person categorical [0]
21 NATIONALITAET_KZ person categorical [-1,0]
22 PRAEGENDE_JUGENDJAHRE person mixed [-1,0]
23 RETOURTYP_BK_S person ordinal [0]
24 SEMIO_SOZ person ordinal [-1,9]
25 SEMIO_FAM person ordinal [-1,9]
26 SEMIO_REL person ordinal [-1,9]
27 SEMIO_MAT person ordinal [-1,9]
28 SEMIO_VERT person ordinal [-1,9]
29 SEMIO_LUST person ordinal [-1,9]
.. ... ... ... ...
55 OST_WEST_KZ building categorical [-1]
56 WOHNLAGE building mixed [-1]
57 CAMEO_DEUG_2015 microcell_rr4 categorical [-1,X]
58 CAMEO_DEU_2015 microcell_rr4 categorical [XX]
59 CAMEO_INTL_2015 microcell_rr4 mixed [-1,XX]
60 KBA05_ANTG1 microcell_rr3 ordinal [-1]
61 KBA05_ANTG2 microcell_rr3 ordinal [-1]
62 KBA05_ANTG3 microcell_rr3 ordinal [-1]
63 KBA05_ANTG4 microcell_rr3 ordinal [-1]
64 KBA05_BAUMAX microcell_rr3 mixed [-1,0]
65 KBA05_GBZ microcell_rr3 ordinal [-1,0]
66 BALLRAUM postcode ordinal [-1]
67 EWDICHTE postcode ordinal [-1]
68 INNENSTADT postcode ordinal [-1]
69 GEBAEUDETYP_RASTER region_rr1 ordinal []
70 KKK region_rr1 ordinal [-1,0]
71 MOBI_REGIO region_rr1 ordinal []
72 ONLINE_AFFINITAET region_rr1 ordinal []
73 REGIOTYP region_rr1 ordinal [-1,0]
74 KBA13_ANZAHL_PKW macrocell_plz8 numeric []
75 PLZ8_ANTG1 macrocell_plz8 ordinal [-1]
76 PLZ8_ANTG2 macrocell_plz8 ordinal [-1]
77 PLZ8_ANTG3 macrocell_plz8 ordinal [-1]
78 PLZ8_ANTG4 macrocell_plz8 ordinal [-1]
79 PLZ8_BAUMAX macrocell_plz8 mixed [-1,0]
80 PLZ8_HHZ macrocell_plz8 ordinal [-1]
81 PLZ8_GBZ macrocell_plz8 ordinal [-1]
82 ARBEIT community ordinal [-1,9]
83 ORTSGR_KLS9 community ordinal [-1,0]
84 RELAT_AB community ordinal [-1,9]
[85 rows x 4 columns]
mixed = feat_info[feat_info['type'] == 'mixed']
print(len(mixed))
print(mixed)
7
attribute information_level type missing_or_unknown
15 LP_LEBENSPHASE_FEIN person mixed [0]
16 LP_LEBENSPHASE_GROB person mixed [0]
22 PRAEGENDE_JUGENDJAHRE person mixed [-1,0]
56 WOHNLAGE building mixed [-1]
59 CAMEO_INTL_2015 microcell_rr4 mixed [-1,XX]
64 KBA05_BAUMAX microcell_rr3 mixed [-1,0]
79 PLZ8_BAUMAX macrocell_plz8 mixed [-1,0]
categorical = feat_info[feat_info['type'] == 'categorical']
print(len(categorical))
print(categorical)
21
attribute information_level type missing_or_unknown
0 AGER_TYP person categorical [-1,0]
2 ANREDE_KZ person categorical [-1,0]
3 CJT_GESAMTTYP person categorical [0]
10 FINANZTYP person categorical [-1]
12 GFK_URLAUBERTYP person categorical []
13 GREEN_AVANTGARDE person categorical []
17 LP_FAMILIE_FEIN person categorical [0]
18 LP_FAMILIE_GROB person categorical [0]
19 LP_STATUS_FEIN person categorical [0]
20 LP_STATUS_GROB person categorical [0]
21 NATIONALITAET_KZ person categorical [-1,0]
38 SHOPPER_TYP person categorical [-1]
39 SOHO_KZ person categorical [-1]
40 TITEL_KZ person categorical [-1,0]
41 VERS_TYP person categorical [-1]
42 ZABEOTYP person categorical [-1,9]
47 KK_KUNDENTYP household categorical [-1]
52 GEBAEUDETYP building categorical [-1,0]
55 OST_WEST_KZ building categorical [-1]
57 CAMEO_DEUG_2015 microcell_rr4 categorical [-1,X]
58 CAMEO_DEU_2015 microcell_rr4 categorical [XX]
Based off of the cell above, we can see that we have the following categories:
For categorical data, you would ordinarily need to encode the levels as dummy variables. Depending on the number of categories, perform one of the following:
# Assess categorical variables: which are binary, which are multi-level, and
# which one needs to be re-encoded?
from sklearn.preprocessing import LabelEncoder
labelencoder = LabelEncoder()
azdias = azdias.drop('CJT_GESAMTTYP', axis=1)
azdias = azdias.drop('FINANZTYP', axis=1)
azdias = azdias.drop('GFK_URLAUBERTYP', axis=1)
azdias = azdias.drop('LP_FAMILIE_FEIN', axis=1)
azdias = azdias.drop('LP_FAMILIE_GROB', axis=1)
azdias = azdias.drop('LP_STATUS_FEIN', axis=1)
azdias = azdias.drop('LP_STATUS_GROB', axis=1)
azdias = azdias.drop('NATIONALITAET_KZ', axis=1)
azdias = azdias.drop('SHOPPER_TYP', axis=1)
azdias = azdias.drop('ZABEOTYP', axis=1)
azdias = azdias.drop('GEBAEUDETYP', axis=1)
azdias = azdias.drop('CAMEO_DEUG_2015', axis=1)
azdias = azdias.drop('CAMEO_DEU_2015', axis=1)
azdias['OST_WEST_KZ'] = azdias['OST_WEST_KZ'].replace({'O': 0,
'W': 1})
print(azdias['OST_WEST_KZ'].head())
604885 1 536670 1 604888 1 624663 0 853635 1 Name: OST_WEST_KZ, dtype: int64
plt.figure(figsize=(20,6))
ax = sns.countplot(azdias.dtypes)
ax.set_xticklabels(ax.get_xticklabels(), rotation=40, ha="right")
plt.show()
Categorical:
There are a handful of features that are marked as "mixed" in the feature summary that require special treatment in order to be included in the analysis. There are two in particular that deserve attention; the handling of the rest are up to your own choices:
Be sure to check Data_Dictionary.md for the details needed to finish these tasks.
# Investigate "PRAEGENDE_JUGENDJAHRE" and engineer two new variables.
print('First few rows to understand what is in dataset')
print(azdias['PRAEGENDE_JUGENDJAHRE'].tail())
#Based off of what I am seeing in the documentation, there is nothing to modify on this
First few rows to understand what is in dataset 349047 8.0 349048 12.0 349049 12.0 349050 14.0 891220 3.0 Name: PRAEGENDE_JUGENDJAHRE, dtype: float64
# re-engineer PRAEGENDE_JUGENDJAHRE
decade_dict = {1: 1, 2: 1, 3: 2, 4: 2, 5: 3, 6: 3, 7: 3,
8: 4, 9: 4, 10: 5, 11: 5, 12: 5, 13: 5,
14: 6, 15: 6
}
movement_dict = {1: 1, 3: 1, 5: 1, 8: 1, 10: 1, 12: 1, 14: 1,
2: 2, 4: 2, 6: 2, 7: 2, 9: 2, 11: 2, 13: 2, 15: 2
}
azdias['DECADE'] = azdias['PRAEGENDE_JUGENDJAHRE'].map(decade_dict)
azdias['MOVEMENT'] = azdias['PRAEGENDE_JUGENDJAHRE'].map(movement_dict)
# Investigate "CAMEO_INTL_2015" and engineer two new variables.
print('First few rows to understand what is in dataset')
print(azdias['CAMEO_INTL_2015'])
First few rows to understand what is in dataset
604885 51
536670 22
604888 51
624663 41
853635 14
625621 45
604886 34
536668 51
625620 51
843481 54
624353 43
608187 45
536669 41
608188 22
604880 41
534987 51
885994 22
624351 13
535385 24
604874 44
852597 41
852598 24
536674 35
853637 51
624606 14
886213 51
625625 41
625624 41
534985 14
534986 43
..
349076 14
349078 51
349079 55
349081 44
349083 51
349084 24
349085 41
349054 45
349052 45
349028 43
349037 44
349029 24
349030 43
349031 33
349032 51
349033 41
349034 51
349035 24
349036 54
349041 45
349051 24
349043 54
349044 41
349045 51
349046 24
349047 51
349048 33
349049 44
349050 41
891220 43
Name: CAMEO_INTL_2015, Length: 623209, dtype: object
# re-engineer "CAMEO_INTL_2015"
ones_place = []
tens_place = []
for x in azdias['CAMEO_INTL_2015'].iteritems():
print(x)
ones_place.append(int(x[1][0]))
tens_place.append(int(x[1][1]))
(604885, '51') (536670, '22') (604888, '51') (624663, '41') (853635, '14') (625621, '45') (604886, '34') (536668, '51') (625620, '51') (843481, '54') (624353, '43') (608187, '45') (536669, '41') (608188, '22') (604880, '41') (534987, '51') (885994, '22') (624351, '13') (535385, '24') (604874, '44') (852597, '41') (852598, '24') (536674, '35') (853637, '51') (624606, '14') (886213, '51') (625625, '41') (625624, '41') (534985, '14') (534986, '43') (604876, '51') (604884, '34') (625623, '51') (604877, '34') (604878, '41') (604879, '23') (608189, '41') (604889, '41') (604881, '22') (604882, '13') (536673, '24') (536672, '25') (604883, '41') (624352, '24') (885462, '22') (853634, '51') (534991, '51') (525433, '25') (853626, '52') (536654, '41') (852162, '54') (536656, '43') (844149, '54') (536657, '24') (536658, '24') (853628, '34') (525444, '43') (604901, '24') (604900, '24') (525443, '51') (885464, '41') (607311, '41') (853629, '55') (525442, '25') (853627, '24') (853625, '14') (852161, '23') (536653, '15') (604906, '51') (534992, '45') (852163, '14') (885465, '54') (625609, '51') (853622, '54') (625611, '25') (536649, '24') (625612, '25') (604905, '32') (843484, '41') (604904, '45') (536652, '15') (625613, '41') (625614, '51') (536660, '14') (525441, '23') (536667, '51') (886212, '55') (608183, '24') (536665, '24') (535386, '41') (525438, '35') (886033, '41') (852160, '24') (890520, '51') (604892, '54') (534989, '54') (525979, '31') (843482, '51') (536666, '54') (608186, '51') (534988, '41') (885463, '24') (625618, '34') (536664, '51') (608179, '45') (843986, '41') (608180, '14') (604897, '15') (525440, '51') (608181, '54') (853631, '34') (536661, '25') (604894, '22') (853632, '13') (625615, '34') (608182, '43') (843483, '54') (625617, '54') (536663, '23') (525439, '54') (853633, '24') (604873, '41') (534982, '54') (625626, '51') (607319, '55') (852517, '14') (525422, '24') (852518, '33') (536686, '51') (525421, '41') (536687, '22') (604840, '43') (853652, '55') (525423, '15') (853653, '41') (534973, '14') (536688, '33') (885451, '25') (853655, '51') (625641, '52') (625642, '24') (853651, '24') (608197, '41') (853656, '51') (604846, '32') (852594, '23') (526162, '13') (534975, '51') (536683, '52') (604848, '24') (525426, '34') (853650, '51') (525425, '23') (534974, '43') (525424, '41') (604845, '34') (885454, '25') (536684, '41') (625640, '41') (885453, '22') (604842, '54') (852154, '43') (534972, '52') (608191, '25') (890522, '52') (852592, '54') (885449, '51') (853663, '52') (853664, '24') (853665, '24') (536691, '44') (604831, '51') (885448, '23') (607320, '35') (604830, '51') (526165, '32') (526166, '41') (885447, '34') (843953, '13') (604829, '41') (843476, '55') (843477, '51') (604833, '54') (534971, '24') (853659, '25') (885450, '14') (526163, '14') (843478, '45') (604837, '24') (853658, '52') (625643, '31') (604836, '25') (853660, '41') (525980, '34') (625644, '22') (607450, '24') (526164, '52') (844158, '43') (853661, '14') (625645, '43') (853662, '14') (526161, '25') (624345, '24') (885455, '25') (534979, '54') (608194, '14') (534981, '41') (625631, '41') (853641, '41') (604867, '54') (853642, '52') (852156, '23') (885461, '45') (625629, '41') (853643, '24') (625632, '32') (536679, '22') (844152, '52') (604865, '55') (852595, '23') (525430, '24') (852157, '41') (890352, '55') (526160, '32') (844151, '41') (536676, '14') (890521, '55') (625627, '41') (604872, '43') (604871, '51') (843480, '25') (608192, '41') (608193, '33') (604908, '24') (853640, '45') (535384, '14') (607313, '51') (534983, '51') (536677, '14') (604869, '23') (536678, '51') (886215, '14') (607315, '24') (525429, '52') (604852, '54') (625636, '24') (844154, '22') (534976, '41') (525428, '51') (844155, '41') (607317, '34') (885457, '14') (625637, '54') (534978, '43') (885456, '14') (536682, '43') (607318, '51') (525427, '44') (843952, '12') (890341, '24') (625639, '51') (604854, '25') (625635, '24') (853648, '41') (625634, '13') (604864, '33') (534977, '35') (604863, '41') (604862, '24') (853644, '24') (604860, '51') (853645, '51') (604858, '43') (853646, '41') (844153, '41') (607316, '54') (885459, '51') (624346, '51') (885458, '51') (853647, '24') (604907, '44') (535498, '23') (625608, '24') (535005, '14') (625585, '22') (604979, '43') (890220, '14') (853588, '24') (536616, '24') (853590, '41') (535006, '41') (536617, '24') (604980, '51') (844146, '13') (604978, '54') (853593, '45') (843950, '51') (843987, '41') (604977, '54') (853595, '51') (852178, '14') (525460, '44') (604976, '51') (843492, '14') (608142, '41') (625583, '45') (525461, '33') (844143, '51') (604984, '51') (853586, '24') (604982, '51') (844144, '24') (853587, '54') (843491, '25') (536614, '24') (608144, '25') (852180, '24') (608146, '14') (844145, '51') (536615, '24') (536618, '13') (536619, '32') (536613, '14') (525457, '45') (853601, '24') (604965, '51') (852173, '14') (885485, '25') (853602, '24') (525458, '43') (885484, '31') (526153, '54') (526152, '22') (890518, '12') (535391, '41') (608154, '51') (536621, '41') (852172, '24') (853603, '24') (535388, '24') (535002, '25') (607452, '51') (853596, '54') (525459, '24') (604974, '52') (853597, '25') (604972, '51') (604971, '54') (852176, '22') (535004, '14') (852174, '22') (843951, '43') (624666, '54') (604970, '41') (853598, '15') (536620, '14') (853599, '43') (885486, '54') (604967, '24') (853600, '41') (852181, '14') (525462, '51') (604962, '51') (624370, '51') (853577, '51') (605005, '51') (624371, '51') (608136, '13') (605004, '41') (605003, '51') (624667, '43') (886204, '54') (852185, '43') (535009, '12') (625580, '44') (605002, '51') (536605, '14') (525975, '43') (625581, '12') (536606, '22') (535306, '51') (853576, '24') (536607, '51') (607453, '51') (625579, '41') (525467, '24') (535012, '14') (525466, '13') (536603, '22') (605013, '24') (853574, '43') (536604, '23') (843494, '55') (885488, '51') (853575, '45') (605011, '14') (605010, '13') (605009, '51') (886203, '14') 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'24') (348759, '41') (348761, '54') (348762, '22') (348814, '41') (348804, '43') (348805, '23') (348806, '41') (348807, '44') (348808, '51') (348809, '55') (348810, '54') (348813, '54') (348815, '44') (348801, '45') (348816, '41') (348817, '34') (348818, '54') (348819, '51') (348820, '43') (348821, '43') (348822, '24') (348823, '32') (348802, '43') (348796, '12') (348764, '41') (348779, '25') (348765, '43') (348766, '54') (348768, '25') (348769, '34') (348771, '41') (348774, '14') (348775, '43') (348776, '54') (348780, '41') (348795, '25') (348782, '14') (348783, '13') (348785, '24') (348787, '41') (348788, '41') (348789, '24') (348790, '25') (348791, '54') (348965, '22') (348967, '51') (349222, '22') (349158, '51') (349119, '43') (349122, '51') (349124, '51') (349125, '13') (349126, '13') (349127, '43') (349128, '55') (349129, '51') (349131, '43') (349132, '54') (349133, '54') (349134, '41') (349136, '43') (349137, '41') (349139, '43') (349140, '24') (349143, '15') (349145, '32') (349150, '43') (349118, '41') (349117, '41') (349116, '14') (349100, '22') (349091, '14') (349092, '43') (349094, '41') (349095, '32') (349096, '13') (349097, '24') (349098, '13') (349099, '43') (349101, '41') (349114, '24') (349102, '43') (349104, '24') (349105, '14') (349106, '14') (349109, '23') (349110, '34') (349111, '25') (349112, '41') (349157, '14') (349159, '24') (348968, '41') (349161, '25') (349193, '34') (349194, '54') (349195, '51') (349196, '41') (349197, '54') (349198, '32') (349199, '45') (349201, '43') (349203, '52') (349204, '51') (349205, '24') (349206, '51') (349207, '14') (349211, '43') (349213, '41') (349215, '54') (349219, '41') (349220, '43') (349221, '23') (349192, '54') (349191, '51') (349189, '41') (349175, '25') (349162, '41') (349167, '34') (349168, '41') (349169, '23') (349170, '41') (349172, '24') (349173, '52') (349174, '41') (349178, '23') (349188, '24') (349179, '41') (349180, '54') (349181, '45') (349182, '51') (349183, '51') (349185, '43') (349186, '14') (349187, '24') (349089, '14') (349088, '24') (349087, '14') (349086, '43') (348998, '32') (348999, '41') (349000, '51') (349002, '51') (349004, '51') (349005, '31') (349006, '51') (349007, '45') (349008, '41') (349009, '45') (349010, '51') (349011, '24') (349013, '41') (349014, '54') (349015, '51') (349018, '15') (349019, '22') (349020, '24') (349022, '14') (348997, '44') (348996, '14') (348995, '41') (348984, '45') (348969, '13') (348970, '13') (348972, '13') (348979, '41') (348980, '44') (348981, '41') (348982, '24') (348983, '43') (348985, '34') (348994, '55') (348986, '14') (348987, '43') (348988, '43') (348989, '14') (348990, '41') (348991, '34') (348992, '45') (348993, '33') (349024, '51') (349025, '31') (349027, '41') (349071, '41') (349055, '51') (349059, '43') (349060, '45') (349062, '15') (349063, '45') (349065, '51') (349067, '24') (349068, '45') (349073, '33') (349053, '51') (349075, '45') (349076, '14') (349078, '51') (349079, '55') (349081, '44') (349083, '51') (349084, '24') (349085, '41') (349054, '45') (349052, '45') (349028, '43') (349037, '44') (349029, '24') (349030, '43') (349031, '33') (349032, '51') (349033, '41') (349034, '51') (349035, '24') (349036, '54') (349041, '45') (349051, '24') (349043, '54') (349044, '41') (349045, '51') (349046, '24') (349047, '51') (349048, '33') (349049, '44') (349050, '41') (891220, '43')
print(ones_place[8])
5
#Add ones_place column and tens_place column while dropping 'CAMEO_INTL_2015'
azdias['CAMEO_INTL_2015_ones'] = ones_place
azdias['CAMEO_INTL_2015_tens'] = tens_place
#Drop columns no longer needed
azdias = azdias.drop('CAMEO_INTL_2015', axis=1)
azdias = azdias.drop('LP_LEBENSPHASE_FEIN', axis=1)
azdias = azdias.drop('LP_LEBENSPHASE_GROB', axis=1)
azdias = azdias.drop('PRAEGENDE_JUGENDJAHRE', axis=1)
columns_to_drop = ['CJT_GESAMTTYP', 'FINANZTYP', 'GFK_URLAUBERTYP', 'LP_FAMILIE_FEIN', 'LP_FAMILIE_GROB', 'LP_STATUS_FEIN', 'LP_STATUS_GROB', 'NATIONALITAET_KZ', 'SHOPPER_TYP', 'ZABEOTYP', 'GEBAEUDETYP', 'CAMEO_DEUG_2015', 'CAMEO_DEU_2015', 'CAMEO_INTL_2015', 'LP_LEBENSPHASE_FEIN', 'LP_LEBENSPHASE_GROB', 'PRAEGENDE_JUGENDJAHRE']
for x in columns_to_drop:
if x in azdias.columns:
print(x)
azdias = azdias.drop(x, axis=1)
print(azdias.shape)
(623209, 66)
Mixed:
In order to finish this step up, you need to make sure that your data frame now only has the columns that you want to keep. To summarize, the dataframe should consist of the following:
Make sure that for any new columns that you have engineered, that you've excluded the original columns from the final dataset. Otherwise, their values will interfere with the analysis later on the project. For example, you should not keep "PRAEGENDE_JUGENDJAHRE", since its values won't be useful for the algorithm: only the values derived from it in the engineered features you created should be retained. As a reminder, your data should only be from the subset with few or no missing values.
# If there are other re-engineering tasks you need to perform, make sure you
# take care of them here. (Dealing with missing data will come in step 2.1.)
#Verify that we have columns that are all numeric
plt.figure(figsize=(20,6))
ax = sns.countplot(azdias.dtypes)
ax.set_xticklabels(ax.get_xticklabels(), rotation=40, ha="right")
plt.show()
print(azdias.dtypes)
ALTERSKATEGORIE_GROB float64
ANREDE_KZ int64
FINANZ_MINIMALIST int64
FINANZ_SPARER int64
FINANZ_VORSORGER int64
FINANZ_ANLEGER int64
FINANZ_UNAUFFAELLIGER int64
FINANZ_HAUSBAUER int64
GREEN_AVANTGARDE int64
HEALTH_TYP float64
RETOURTYP_BK_S float64
SEMIO_SOZ int64
SEMIO_FAM int64
SEMIO_REL int64
SEMIO_MAT int64
SEMIO_VERT int64
SEMIO_LUST int64
SEMIO_ERL int64
SEMIO_KULT int64
SEMIO_RAT int64
SEMIO_KRIT int64
SEMIO_DOM int64
SEMIO_KAEM int64
SEMIO_PFLICHT int64
SEMIO_TRADV int64
SOHO_KZ float64
VERS_TYP float64
ANZ_PERSONEN float64
ANZ_TITEL float64
HH_EINKOMMEN_SCORE float64
...
OST_WEST_KZ int64
WOHNLAGE float64
KBA05_ANTG1 float64
KBA05_ANTG2 float64
KBA05_ANTG3 float64
KBA05_ANTG4 float64
KBA05_GBZ float64
BALLRAUM float64
EWDICHTE float64
INNENSTADT float64
GEBAEUDETYP_RASTER float64
KKK float64
MOBI_REGIO float64
ONLINE_AFFINITAET float64
REGIOTYP float64
KBA13_ANZAHL_PKW float64
PLZ8_ANTG1 float64
PLZ8_ANTG2 float64
PLZ8_ANTG3 float64
PLZ8_ANTG4 float64
PLZ8_BAUMAX float64
PLZ8_HHZ float64
PLZ8_GBZ float64
ARBEIT float64
ORTSGR_KLS9 float64
RELAT_AB float64
DECADE int64
MOVEMENT int64
CAMEO_INTL_2015_ones int64
CAMEO_INTL_2015_tens int64
Length: 66, dtype: object
Even though you've finished cleaning up the general population demographics data, it's important to look ahead to the future and realize that you'll need to perform the same cleaning steps on the customer demographics data. In this substep, complete the function below to execute the main feature selection, encoding, and re-engineering steps you performed above. Then, when it comes to looking at the customer data in Step 3, you can just run this function on that DataFrame to get the trimmed dataset in a single step.
def clean_data(df):
"""
Perform feature trimming, re-encoding, and engineering for demographics
data
INPUT: Demographics DataFrame
OUTPUT: Trimmed and cleaned demographics DataFrame
"""
# Put in code here to execute all main cleaning steps:
# convert missing value codes into NaNs, ...
counter = 0
for x in df.iteritems():
col_name = feat_info_missing.loc[feat_info_missing['attribute'] == x[0]]
missing = col_name['missing_or_unknown'][counter]
counter = counter + 1
if(len(missing) > 2):
df[x[0]] = df[x[0]].replace(obtain_missing_info(missing), np.NaN)
# remove selected columns and rows, ...
'''
for column in df:
counts = df[column].isnull().sum()
if(counts >= (df.shape[0] * .3)):
print(column)
df = df.drop(column, axis=1)
print(len(df.columns))
print(df.shape)'''
df = df.drop('AGER_TYP', axis=1)
df = df.drop('GEBURTSJAHR', axis=1)
df = df.drop('TITEL_KZ', axis=1)
df = df.drop('ALTER_HH', axis=1)
df = df.drop('KK_KUNDENTYP', axis=1)
df = df.drop('KBA05_BAUMAX', axis=1)
df = df.dropna(axis=0, inplace=False)
if 'OST_WEST_KZ' in df:
df['OST_WEST_KZ'] = df['OST_WEST_KZ'].replace({'O': 0,
'W': 1})
ones_place = []
tens_place = []
if 'CAMEO_INTL_2015' in df:
for x in df['CAMEO_INTL_2015'].iteritems():
print(x)
ones_place.append(int(x[1][0]))
tens_place.append(int(x[1][1]))
df['CAMEO_INTL_2015_ones'] = ones_place
df['CAMEO_INTL_2015_tens'] = tens_place
decade_dict = {1: 1, 2: 1, 3: 2, 4: 2, 5: 3, 6: 3, 7: 3,
8: 4, 9: 4, 10: 5, 11: 5, 12: 5, 13: 5,
14: 6, 15: 6
}
movement_dict = {1: 1, 3: 1, 5: 1, 8: 1, 10: 1, 12: 1, 14: 1,
2: 2, 4: 2, 6: 2, 7: 2, 9: 2, 11: 2, 13: 2, 15: 2
}
if 'PRAEGENDE_JUGENDJAHRE'in df:
df['DECADE'] = df['PRAEGENDE_JUGENDJAHRE'].map(decade_dict)
df['MOVEMENT'] = df['PRAEGENDE_JUGENDJAHRE'].map(movement_dict)
columns_to_drop = ['CJT_GESAMTTYP', 'FINANZTYP', 'GFK_URLAUBERTYP', 'LP_FAMILIE_FEIN',
'LP_FAMILIE_GROB', 'LP_STATUS_FEIN', 'LP_STATUS_GROB', 'NATIONALITAET_KZ',
'SHOPPER_TYP', 'ZABEOTYP', 'GEBAEUDETYP', 'CAMEO_DEUG_2015', 'CAMEO_DEU_2015',
'CAMEO_INTL_2015', 'LP_LEBENSPHASE_FEIN', 'LP_LEBENSPHASE_GROB', 'PRAEGENDE_JUGENDJAHRE']
for x in columns_to_drop:
print(x)
if x in df.columns:
df = df.drop(x, axis=1)
# Return the cleaned dataframe.
return df
Before we apply dimensionality reduction techniques to the data, we need to perform feature scaling so that the principal component vectors are not influenced by the natural differences in scale for features. Starting from this part of the project, you'll want to keep an eye on the API reference page for sklearn to help you navigate to all of the classes and functions that you'll need. In this substep, you'll need to check the following:
.fit_transform() method to both fit a procedure to the data as well as apply the transformation to the data at the same time. Don't forget to keep the fit sklearn objects handy, since you'll be applying them to the customer demographics data towards the end of the project.# Apply feature scaling to the general population demographics data.
from sklearn.preprocessing import StandardScaler
scaler = StandardScaler(with_mean=True)
scaler.fit_transform(azdias)
array([[-0.77209181, 0.97782476, -1.51222382, ..., -0.5536702 ,
1.14788172, -1.25110753],
[ 0.20210748, 0.97782476, -0.7773472 , ..., -0.5536702 ,
-0.90999737, -0.58413108],
[ 0.20210748, 0.97782476, -0.7773472 , ..., -0.5536702 ,
1.14788172, -1.25110753],
...,
[-0.77209181, -1.02267813, -0.04247059, ..., -0.5536702 ,
0.46192202, 0.74982182],
[-1.7462911 , -1.02267813, -1.51222382, ..., -0.5536702 ,
0.46192202, -1.25110753],
[ 1.17630677, -1.02267813, 0.69240603, ..., -0.5536702 ,
0.46192202, 0.08284537]])
azdias.shape
(623209, 66)
For scaling, I decided to go with the StandardScalar approach with filling mean values in for Imputer
On your scaled data, you are now ready to apply dimensionality reduction techniques.
plot() function. Based on what you find, select a value for the number of transformed features you'll retain for the clustering part of the project.# Apply PCA to the data.
from sklearn.decomposition import PCA
def scree_plot(pca):
num_components = len(pca.explained_variance_ratio_)
ind = np.arange(num_components)
vals = pca.explained_variance_ratio_
plt.figure(figsize=(18, 6))
ax = plt.subplot(111)
cumvals = np.cumsum(vals)
ax.bar(ind, vals)
ax.plot(ind, cumvals)
for i in range(num_components):
ax.annotate(r"%s%%" % ((str(vals[i]*100)[:4])), (ind[i]+0.2, vals[i]), va="bottom", ha="center", fontsize=12)
ax.xaxis.set_tick_params(width=0)
ax.yaxis.set_tick_params(width=2, length=12)
ax.set_xlabel("Principal Component")
ax.set_ylabel("Variance Explained (%)")
plt.title('Explained Variance Per Principal Component')
def do_pca(n_components, data):
'''
Transforms data using PCA to create n_components, and provides back the results of the
transformation.
INPUT: n_components - int - the number of principal components to create
data - the data you would like to transform
OUTPUT: pca - the pca object created after fitting the data
X_pca - the transformed X matrix with new number of components
'''
X = StandardScaler().fit_transform(data)
pca = PCA(n_components)
X_pca = pca.fit_transform(X)
return pca, X_pca
def pca_results(full_dataset, pca):
'''
Create a DataFrame of the PCA results
Includes dimension feature weights and explained variance
Visualizes the PCA results
'''
# Dimension indexing
dimensions = dimensions = ['Dimension {}'.format(i) for i in range(1,len(pca.components_)+1)]
# PCA component
components = pd.DataFrame(np.round(pca.components_, 4), columns = full_dataset.keys())
components.index = dimensions
# PCA explained variance
ratios = pca.explained_variance_ratio_.reshape(len(pca.components_), 1)
variance_ratios = pd.DataFrame(np.round(ratios, 4), columns = ['Explained Variance'])
variance_ratios.index = dimensions
# Create a bar plot visualization
fig, ax = plt.subplots(figsize = (14,8))
# Plot the feature weights as a function of the components
components.plot(ax = ax, kind = 'bar');
ax.set_ylabel("Feature Weights")
ax.set_xticklabels(dimensions, rotation=0)
# Display the explained variance ratios
for i, ev in enumerate(pca.explained_variance_ratio_):
ax.text(i-0.40, ax.get_ylim()[1] + 0.05, "Explained Variance\n %.4f"%(ev))
# Return a concatenated DataFrame
return pd.concat([variance_ratios, components], axis = 1)
# No parameters
pca = PCA()
pca.fit_transform(azdias)
scree_plot(pca)
#20 components
pca, X_pca = do_pca(20, azdias)
scree_plot(pca)
# 40 components
pca, X_pca = do_pca(40, azdias)
scree_plot(pca)
#60 components
pca, X_pca = do_pca(60, azdias)
scree_plot(pca)
# Re-apply PCA to the data while selecting for number of components to retain.
#60 components
pca, X_pca = do_pca(60, azdias)
scree_plot(pca)
As we can see when the number of components is low (i.e. 20-40), we are still seeing a good deal of slop in the amount of variablility explained. As we get to the 65 number of components, we start to see it level off. I decided to go with 60 components as it still had a slight slope.
Now that we have our transformed principal components, it's a nice idea to check out the weight of each variable on the first few components to see if they can be interpreted in some fashion.
As a reminder, each principal component is a unit vector that points in the direction of highest variance (after accounting for the variance captured by earlier principal components). The further a weight is from zero, the more the principal component is in the direction of the corresponding feature. If two features have large weights of the same sign (both positive or both negative), then increases in one tend expect to be associated with increases in the other. To contrast, features with different signs can be expected to show a negative correlation: increases in one variable should result in a decrease in the other.
pd.set_option('display.max_columns', None)
pca_results(azdias, pca)
| Explained Variance | ALTERSKATEGORIE_GROB | ANREDE_KZ | FINANZ_MINIMALIST | FINANZ_SPARER | FINANZ_VORSORGER | FINANZ_ANLEGER | FINANZ_UNAUFFAELLIGER | FINANZ_HAUSBAUER | GREEN_AVANTGARDE | HEALTH_TYP | RETOURTYP_BK_S | SEMIO_SOZ | SEMIO_FAM | SEMIO_REL | SEMIO_MAT | SEMIO_VERT | SEMIO_LUST | SEMIO_ERL | SEMIO_KULT | SEMIO_RAT | SEMIO_KRIT | SEMIO_DOM | SEMIO_KAEM | SEMIO_PFLICHT | SEMIO_TRADV | SOHO_KZ | VERS_TYP | ANZ_PERSONEN | ANZ_TITEL | HH_EINKOMMEN_SCORE | W_KEIT_KIND_HH | WOHNDAUER_2008 | ANZ_HAUSHALTE_AKTIV | ANZ_HH_TITEL | KONSUMNAEHE | MIN_GEBAEUDEJAHR | OST_WEST_KZ | WOHNLAGE | KBA05_ANTG1 | KBA05_ANTG2 | KBA05_ANTG3 | KBA05_ANTG4 | KBA05_GBZ | BALLRAUM | EWDICHTE | INNENSTADT | GEBAEUDETYP_RASTER | KKK | MOBI_REGIO | ONLINE_AFFINITAET | REGIOTYP | KBA13_ANZAHL_PKW | PLZ8_ANTG1 | PLZ8_ANTG2 | PLZ8_ANTG3 | PLZ8_ANTG4 | PLZ8_BAUMAX | PLZ8_HHZ | PLZ8_GBZ | ARBEIT | ORTSGR_KLS9 | RELAT_AB | DECADE | MOVEMENT | CAMEO_INTL_2015_ones | CAMEO_INTL_2015_tens | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Dimension 1 | 0.1772 | -0.1232 | -0.0006 | -0.2089 | 0.1421 | -0.1148 | 0.0655 | 0.0742 | 0.1484 | -0.1083 | 0.0334 | -0.0237 | 0.0466 | 0.0807 | 0.1083 | 0.0836 | -0.0258 | -0.0881 | -0.0863 | 0.0754 | 0.0919 | -0.0008 | 0.0166 | 0.0320 | 0.1112 | 0.0987 | -0.0022 | 0.0205 | -0.0784 | -0.0045 | 0.1898 | 0.0321 | -0.0623 | 0.1317 | 0.0329 | -0.1608 | -0.0355 | -0.0623 | -0.0788 | -0.2184 | 0.0053 | 0.1308 | 0.1488 | -0.2096 | -0.1219 | 0.1886 | -0.1602 | -0.1143 | 0.0415 | -0.2341 | -0.0344 | 0.0698 | -0.0819 | -0.2217 | 0.1451 | 0.2202 | 0.2151 | 0.2119 | 0.0366 | -0.1689 | 0.1408 | 0.1922 | 0.1283 | 0.1034 | -0.1083 | 0.1967 | -0.1231 |
| Dimension 2 | 0.1345 | 0.2586 | 0.0856 | 0.0670 | -0.2338 | 0.2265 | -0.2042 | -0.2246 | 0.1119 | -0.0128 | -0.0525 | 0.1643 | -0.1005 | -0.1776 | -0.2618 | -0.1544 | -0.0641 | 0.1794 | 0.2307 | -0.2172 | -0.1726 | 0.1183 | 0.0665 | 0.1081 | -0.2375 | -0.2291 | -0.0022 | 0.0279 | -0.0599 | 0.0079 | 0.0429 | 0.1159 | 0.0598 | 0.0583 | 0.0296 | -0.0676 | -0.0273 | -0.0305 | -0.0572 | -0.0797 | -0.0097 | 0.0462 | 0.0663 | -0.0870 | -0.0624 | 0.0942 | -0.0775 | -0.0422 | 0.0025 | -0.0879 | -0.1571 | 0.0208 | -0.0383 | -0.0943 | 0.0636 | 0.0964 | 0.0926 | 0.0876 | 0.0119 | -0.0760 | 0.0690 | 0.0943 | 0.0650 | -0.2482 | -0.0128 | 0.0690 | -0.0028 |
| Dimension 3 | 0.0937 | 0.0803 | -0.3683 | 0.1617 | -0.1006 | 0.0964 | -0.1872 | -0.0896 | -0.0547 | 0.0584 | -0.0106 | 0.1131 | 0.2639 | 0.2519 | 0.0782 | 0.0494 | 0.3493 | 0.0723 | -0.1717 | 0.2328 | -0.2175 | -0.2707 | -0.3123 | -0.3386 | -0.0753 | -0.0838 | 0.0006 | 0.0198 | -0.0012 | 0.0109 | -0.0351 | 0.0905 | 0.0355 | 0.0217 | 0.0134 | -0.0355 | -0.0091 | -0.0101 | -0.0241 | -0.0149 | -0.0127 | 0.0017 | 0.0239 | -0.0198 | -0.0347 | 0.0454 | -0.0416 | -0.0287 | -0.0207 | -0.0219 | -0.0498 | -0.0095 | -0.0195 | -0.0400 | 0.0264 | 0.0401 | 0.0412 | 0.0430 | 0.0062 | -0.0330 | 0.0288 | 0.0454 | 0.0277 | -0.1050 | 0.0584 | 0.0167 | -0.0054 |
| Dimension 4 | 0.0558 | -0.0455 | 0.0432 | 0.0610 | 0.0022 | -0.0220 | -0.1167 | 0.0923 | -0.1080 | 0.3792 | 0.0051 | -0.0043 | -0.0047 | -0.0227 | -0.0024 | 0.0208 | -0.0151 | -0.0051 | -0.0191 | -0.0337 | 0.0573 | 0.0169 | 0.1223 | 0.0817 | 0.0234 | 0.0671 | 0.0017 | 0.0163 | 0.0946 | 0.0466 | -0.2648 | -0.0844 | 0.0058 | -0.0390 | 0.0325 | -0.1263 | -0.0466 | 0.1076 | -0.2807 | 0.0997 | 0.0042 | -0.0734 | -0.0372 | 0.0570 | -0.2187 | 0.2487 | -0.2005 | -0.0675 | -0.2578 | 0.0671 | 0.1367 | -0.1967 | 0.0359 | -0.0310 | 0.0925 | 0.0813 | 0.0634 | 0.0484 | 0.1162 | 0.0336 | 0.0536 | 0.2429 | 0.0912 | 0.0442 | 0.3792 | -0.1394 | 0.0707 |
| Dimension 5 | 0.0367 | 0.0040 | 0.0079 | 0.0863 | 0.0000 | -0.0628 | 0.0560 | -0.0453 | -0.0884 | 0.0525 | 0.0069 | -0.0352 | 0.0031 | -0.0358 | -0.0083 | -0.0665 | 0.0021 | -0.0119 | 0.0247 | 0.0115 | -0.0112 | -0.0248 | 0.0062 | 0.0265 | -0.0032 | -0.0291 | 0.0036 | 0.0013 | 0.1391 | -0.0017 | -0.0631 | -0.1284 | 0.0427 | -0.0206 | -0.0228 | 0.1253 | 0.0970 | -0.2154 | 0.0038 | 0.0984 | -0.1353 | -0.0841 | 0.0061 | 0.0933 | -0.0246 | 0.0209 | -0.0625 | 0.0485 | 0.1325 | 0.1032 | 0.1166 | 0.0823 | -0.5114 | -0.0229 | -0.1183 | -0.0352 | 0.0200 | 0.0930 | -0.4935 | -0.3993 | 0.1883 | 0.0701 | 0.1189 | 0.0334 | 0.0525 | -0.0132 | 0.0272 |
| Dimension 6 | 0.0318 | -0.0014 | 0.0261 | -0.0239 | 0.0025 | -0.0319 | 0.0186 | -0.0334 | 0.0403 | 0.0332 | -0.0415 | -0.0227 | 0.0115 | -0.0022 | -0.0084 | 0.0164 | -0.0083 | 0.0300 | 0.0000 | -0.0426 | 0.0234 | -0.0188 | -0.0150 | -0.0185 | -0.0276 | 0.0330 | 0.0009 | -0.0558 | 0.0361 | 0.0735 | -0.0817 | -0.0365 | 0.0106 | 0.3568 | 0.2480 | -0.0272 | 0.0215 | -0.1315 | 0.1510 | -0.0156 | -0.3659 | -0.2042 | 0.4034 | -0.1343 | 0.0070 | -0.1024 | 0.0324 | -0.2202 | -0.2222 | -0.0871 | 0.0346 | -0.2292 | 0.0291 | 0.0107 | -0.2518 | -0.0723 | 0.1113 | 0.1063 | 0.0103 | -0.0728 | -0.2010 | -0.0951 | -0.2311 | 0.0047 | 0.0332 | -0.0727 | 0.0366 |
| Dimension 7 | 0.0275 | 0.0186 | -0.0600 | 0.0455 | 0.0637 | -0.0134 | 0.0733 | 0.0493 | -0.1902 | -0.0327 | 0.2357 | -0.0034 | 0.0516 | -0.0388 | -0.0571 | -0.2780 | 0.0126 | -0.0453 | 0.0313 | 0.0318 | -0.1419 | 0.0107 | 0.0050 | 0.0321 | -0.0133 | -0.1596 | 0.0062 | 0.2590 | 0.2076 | -0.0284 | -0.0085 | -0.2049 | 0.0428 | 0.1274 | 0.0097 | 0.0282 | -0.0480 | 0.1526 | -0.0335 | 0.0639 | -0.2158 | -0.1132 | 0.1906 | -0.0705 | -0.1098 | 0.0986 | -0.0881 | 0.0433 | 0.3650 | -0.0111 | 0.1482 | 0.3632 | 0.1781 | 0.0691 | -0.0943 | -0.0303 | 0.0389 | -0.0255 | 0.1978 | 0.1205 | -0.0080 | 0.1121 | 0.0170 | 0.1031 | -0.0327 | 0.0153 | -0.0642 |
| Dimension 8 | 0.0245 | -0.1226 | 0.0118 | 0.0357 | -0.0856 | 0.1242 | -0.1382 | -0.0186 | -0.0004 | -0.0490 | 0.0714 | 0.1474 | -0.0184 | 0.0408 | 0.1245 | 0.0655 | -0.0603 | -0.0991 | -0.0879 | 0.0866 | 0.1398 | 0.1213 | 0.0550 | 0.0521 | 0.1582 | 0.1417 | -0.0072 | 0.0397 | -0.3475 | 0.0013 | 0.0037 | 0.3395 | -0.0446 | 0.1318 | 0.0843 | 0.0704 | -0.1641 | 0.2283 | -0.1129 | 0.1007 | -0.0906 | -0.1713 | 0.1140 | 0.0062 | -0.1632 | 0.1211 | -0.1171 | 0.0447 | 0.0841 | 0.0320 | -0.2631 | 0.1456 | -0.1205 | 0.1955 | -0.1502 | -0.1803 | -0.1220 | -0.1317 | -0.1391 | 0.0002 | -0.0201 | 0.1151 | 0.0288 | -0.1088 | -0.0490 | -0.0852 | 0.0637 |
| Dimension 9 | 0.0229 | 0.0027 | 0.0915 | 0.0414 | -0.1079 | 0.0868 | -0.0195 | -0.1139 | 0.0756 | 0.0095 | -0.4465 | 0.0173 | -0.0569 | -0.0046 | 0.1213 | 0.2319 | -0.0020 | 0.1021 | 0.0314 | 0.0625 | 0.1860 | -0.1218 | -0.0581 | 0.0764 | 0.0950 | 0.1310 | 0.0104 | -0.4438 | 0.2359 | -0.0114 | -0.0141 | -0.0923 | 0.2044 | 0.0347 | -0.0309 | 0.0712 | -0.0105 | -0.0856 | -0.0274 | 0.0395 | -0.1377 | -0.0325 | 0.0775 | -0.0262 | -0.0349 | 0.0366 | -0.0437 | 0.1219 | 0.2235 | 0.0148 | 0.0432 | 0.2270 | 0.1355 | 0.0074 | -0.0570 | 0.0151 | 0.0316 | -0.0219 | 0.1620 | 0.0937 | 0.1485 | 0.0691 | 0.0711 | -0.1307 | 0.0095 | 0.0246 | 0.0449 |
| Dimension 10 | 0.0209 | 0.0353 | 0.0141 | 0.0319 | -0.0302 | 0.1215 | -0.1069 | 0.0658 | -0.1152 | -0.0484 | -0.0824 | 0.0701 | -0.0428 | 0.0065 | 0.0074 | 0.1085 | 0.0027 | 0.0544 | 0.0337 | 0.0035 | 0.0512 | -0.0178 | 0.0005 | 0.0245 | 0.0323 | 0.0333 | 0.0110 | -0.1082 | 0.2394 | 0.0370 | 0.0261 | -0.1928 | 0.1080 | -0.0002 | 0.0375 | -0.1449 | -0.2332 | 0.4866 | 0.1215 | -0.0353 | 0.1659 | 0.0037 | -0.0356 | -0.0319 | -0.0628 | 0.0280 | -0.0118 | -0.1584 | 0.0079 | -0.0440 | 0.0731 | 0.0901 | -0.1545 | -0.0039 | 0.1680 | 0.0012 | -0.0155 | 0.0412 | -0.2232 | -0.1591 | -0.4147 | -0.0704 | -0.1654 | -0.0116 | -0.0484 | 0.0606 | -0.2256 |
| Dimension 11 | 0.0200 | 0.1158 | 0.0054 | -0.2198 | 0.1723 | -0.1159 | 0.1183 | 0.2681 | 0.1744 | 0.1159 | -0.3602 | -0.2764 | 0.0396 | -0.0459 | -0.0856 | -0.1229 | 0.0638 | 0.1905 | 0.0679 | -0.0834 | -0.1667 | -0.0916 | -0.1764 | -0.0473 | -0.1359 | -0.1622 | 0.0048 | -0.1256 | -0.1037 | 0.0789 | 0.0419 | 0.1725 | -0.2459 | 0.0878 | 0.1418 | 0.0394 | -0.2097 | 0.1381 | -0.1063 | -0.0186 | 0.0521 | 0.0289 | 0.0138 | -0.0635 | -0.0510 | 0.0336 | -0.0002 | 0.0589 | 0.0588 | -0.0475 | 0.0988 | 0.1045 | -0.0700 | 0.1192 | -0.0315 | -0.0879 | -0.0990 | -0.1077 | -0.0999 | 0.0039 | -0.0150 | 0.0519 | 0.0299 | 0.1088 | 0.1159 | -0.0351 | 0.0850 |
| Dimension 12 | 0.0191 | -0.0523 | -0.0158 | -0.0789 | -0.0351 | 0.1069 | -0.0475 | -0.0837 | 0.1334 | -0.0441 | 0.1017 | 0.0508 | 0.0355 | 0.0112 | 0.0059 | -0.0178 | 0.0097 | -0.1438 | -0.0475 | -0.0010 | 0.0027 | -0.0723 | 0.0684 | -0.0075 | 0.0054 | 0.0301 | 0.0188 | 0.1394 | 0.2626 | 0.2164 | 0.0900 | -0.2493 | 0.2004 | 0.1230 | 0.2524 | 0.1836 | -0.1934 | 0.0410 | -0.1698 | -0.1804 | 0.0737 | 0.2597 | 0.0088 | -0.1998 | 0.0451 | -0.0009 | 0.0793 | 0.2426 | -0.1192 | -0.1587 | 0.0208 | -0.2066 | -0.0431 | 0.1273 | -0.0305 | -0.0861 | -0.1332 | -0.1985 | -0.0971 | 0.0423 | 0.1103 | 0.0134 | 0.1437 | -0.0437 | -0.0441 | -0.0264 | 0.2160 |
| Dimension 13 | 0.0184 | -0.0056 | 0.0040 | 0.0732 | -0.0133 | -0.0245 | 0.0416 | -0.0178 | -0.0809 | 0.0380 | 0.0378 | -0.0070 | -0.0385 | 0.0056 | 0.0147 | 0.0348 | -0.0165 | 0.0292 | 0.0099 | 0.0268 | 0.0255 | 0.0430 | 0.0099 | 0.0029 | 0.0326 | 0.0038 | -0.0023 | 0.0132 | -0.0319 | 0.5963 | 0.0011 | 0.0543 | -0.0007 | 0.0900 | 0.5476 | -0.0933 | 0.0793 | -0.0356 | 0.0737 | 0.0926 | 0.1526 | -0.1626 | -0.1165 | 0.1670 | 0.1476 | -0.0529 | 0.0898 | -0.1098 | 0.1265 | 0.1090 | -0.0482 | 0.1445 | 0.0231 | -0.0840 | 0.1168 | 0.0499 | 0.0098 | 0.0529 | 0.0698 | 0.0262 | 0.1230 | -0.0405 | 0.1470 | -0.0032 | 0.0380 | 0.0861 | -0.0973 |
| Dimension 14 | 0.0163 | -0.0463 | 0.0099 | -0.0323 | -0.0231 | 0.0070 | 0.0234 | -0.0565 | 0.1147 | -0.0860 | -0.0248 | 0.0502 | 0.0372 | -0.0198 | 0.0359 | -0.0664 | -0.0136 | 0.0061 | -0.0342 | 0.0175 | 0.0139 | -0.0106 | -0.0401 | 0.0191 | 0.0279 | 0.0038 | 0.0088 | 0.0680 | 0.0327 | 0.2559 | -0.0608 | 0.0477 | -0.0245 | -0.1225 | 0.0996 | 0.0024 | 0.1837 | -0.2079 | 0.0656 | -0.0514 | 0.0874 | 0.2650 | -0.2096 | 0.0176 | -0.3480 | 0.0838 | -0.2770 | -0.0002 | 0.1095 | 0.0193 | 0.0796 | 0.1284 | 0.0466 | -0.0016 | -0.0836 | 0.0152 | 0.0223 | 0.0520 | -0.0041 | -0.0437 | -0.2246 | 0.0687 | -0.4630 | -0.0319 | -0.0860 | -0.2070 | 0.2688 |
| Dimension 15 | 0.0158 | 0.0940 | -0.0518 | 0.0390 | -0.0148 | -0.0434 | -0.0933 | -0.0505 | -0.0689 | -0.3723 | 0.0098 | 0.0218 | -0.0748 | 0.0243 | -0.0448 | 0.1360 | 0.0489 | 0.0727 | 0.0452 | -0.0015 | -0.0344 | -0.0117 | 0.0153 | -0.0129 | -0.0678 | -0.0251 | -0.0096 | -0.1190 | 0.0569 | -0.1207 | 0.1079 | -0.2290 | -0.3445 | 0.0932 | 0.1104 | -0.0754 | 0.0011 | -0.0624 | -0.0335 | 0.0600 | 0.1921 | -0.2279 | -0.0364 | 0.1291 | -0.2048 | 0.0931 | -0.1501 | -0.1484 | -0.1487 | 0.0791 | 0.2096 | -0.1421 | 0.0077 | 0.0661 | -0.0717 | -0.1108 | -0.1039 | -0.0649 | 0.0315 | 0.0906 | 0.1610 | 0.1102 | 0.1156 | 0.0297 | -0.3723 | -0.0403 | 0.0577 |
| Dimension 16 | 0.0151 | -0.0063 | 0.0012 | 0.0009 | -0.0043 | 0.0051 | -0.0017 | -0.0018 | 0.0106 | -0.0086 | -0.0020 | -0.0087 | 0.0007 | -0.0011 | 0.0036 | -0.0072 | -0.0023 | 0.0032 | -0.0050 | -0.0012 | 0.0011 | 0.0043 | -0.0016 | -0.0016 | 0.0044 | 0.0036 | 0.9986 | 0.0170 | -0.0080 | -0.0145 | -0.0019 | 0.0140 | -0.0059 | 0.0005 | -0.0030 | -0.0106 | -0.0079 | -0.0039 | 0.0019 | 0.0092 | 0.0033 | -0.0180 | -0.0013 | 0.0117 | 0.0076 | -0.0011 | 0.0041 | -0.0110 | -0.0030 | 0.0096 | 0.0028 | -0.0024 | 0.0006 | -0.0061 | 0.0049 | 0.0050 | 0.0057 | 0.0069 | 0.0044 | -0.0008 | 0.0048 | -0.0016 | 0.0065 | -0.0038 | -0.0086 | -0.0034 | 0.0074 |
| Dimension 17 | 0.0145 | 0.1461 | -0.0473 | 0.0376 | 0.0814 | -0.1430 | -0.0268 | 0.1069 | -0.3441 | 0.0293 | 0.0872 | 0.1388 | -0.0205 | 0.0235 | -0.0734 | 0.1831 | 0.0559 | 0.0457 | 0.1080 | 0.0051 | -0.0297 | 0.0626 | 0.0563 | 0.0275 | -0.0784 | -0.0559 | 0.0393 | -0.3158 | -0.1854 | 0.1390 | 0.0369 | -0.0929 | -0.0335 | 0.0144 | 0.0435 | 0.1528 | 0.5019 | 0.1538 | -0.0606 | -0.1269 | -0.1195 | 0.2243 | 0.0433 | -0.1404 | -0.0717 | 0.0462 | -0.0632 | 0.1958 | -0.0404 | -0.1247 | -0.1038 | -0.0328 | -0.0060 | 0.0676 | -0.0475 | -0.0489 | -0.0440 | -0.0884 | -0.0371 | 0.0226 | -0.0420 | 0.0327 | 0.0060 | 0.1088 | 0.0293 | 0.0437 | -0.1577 |
| Dimension 18 | 0.0140 | -0.0363 | 0.0117 | 0.1133 | -0.1511 | 0.1834 | -0.1166 | -0.1368 | -0.0253 | 0.0281 | 0.0438 | -0.0192 | 0.0051 | -0.0129 | 0.0359 | 0.0031 | -0.0286 | -0.1326 | -0.0304 | 0.0405 | 0.0579 | 0.0148 | 0.0501 | 0.0168 | 0.0467 | 0.0422 | -0.0028 | -0.0712 | -0.0276 | 0.0630 | -0.0461 | 0.0031 | -0.6769 | -0.0127 | 0.0206 | 0.0911 | -0.0594 | 0.1003 | -0.0279 | 0.0026 | -0.2294 | 0.1500 | 0.0136 | -0.0520 | 0.1597 | -0.0458 | 0.1276 | 0.1986 | 0.0615 | -0.0255 | 0.3272 | 0.0416 | 0.0185 | -0.0948 | 0.1262 | 0.1337 | 0.1118 | 0.0605 | 0.0076 | -0.0717 | -0.0854 | -0.0590 | 0.0047 | -0.0940 | 0.0281 | 0.0029 | 0.0865 |
| Dimension 19 | 0.0130 | 0.0814 | -0.0370 | 0.0750 | 0.0785 | -0.1999 | 0.0408 | 0.1029 | -0.1986 | -0.1726 | 0.1124 | 0.0495 | 0.0343 | -0.0224 | -0.0601 | 0.0435 | 0.0490 | -0.0087 | 0.0578 | 0.0163 | -0.0495 | 0.0544 | 0.0323 | 0.0082 | -0.0626 | -0.0676 | 0.0017 | -0.2584 | -0.1535 | 0.1752 | -0.0334 | -0.0414 | 0.1533 | -0.1528 | -0.0388 | -0.0069 | -0.5596 | -0.0490 | 0.0281 | 0.1201 | -0.2819 | 0.1032 | -0.0525 | 0.0494 | 0.0077 | 0.0006 | -0.0085 | 0.0939 | -0.0368 | 0.0932 | -0.1402 | -0.0655 | 0.0230 | -0.0929 | 0.0593 | 0.1257 | 0.1226 | 0.1154 | 0.0524 | -0.0503 | -0.0017 | -0.0154 | 0.0098 | 0.1036 | -0.1726 | -0.1201 | 0.2381 |
| Dimension 20 | 0.0126 | -0.0045 | -0.0011 | 0.0055 | 0.0141 | -0.0148 | -0.0006 | 0.1174 | -0.1179 | -0.1073 | -0.0853 | -0.0575 | 0.0115 | 0.0041 | 0.0069 | 0.0090 | 0.0221 | 0.0714 | 0.0019 | 0.0056 | 0.0012 | 0.0220 | 0.0124 | 0.0045 | 0.0016 | 0.0149 | -0.0139 | 0.0740 | -0.0079 | -0.3351 | -0.0260 | 0.0360 | 0.1540 | 0.1500 | 0.2420 | 0.0016 | 0.3023 | 0.1709 | -0.1157 | 0.0359 | 0.0756 | -0.1416 | 0.0535 | -0.0157 | 0.1192 | 0.0054 | 0.1078 | 0.1234 | 0.0378 | 0.0151 | -0.0502 | 0.0605 | -0.0019 | -0.1376 | 0.3169 | 0.1593 | 0.0782 | 0.0509 | -0.0208 | -0.0945 | -0.1054 | -0.0424 | 0.0242 | 0.0148 | -0.1073 | -0.1729 | 0.5359 |
| Dimension 21 | 0.0122 | -0.0536 | 0.0279 | -0.0632 | 0.0046 | 0.0916 | -0.0685 | 0.1200 | 0.0714 | -0.2445 | -0.2921 | -0.0913 | 0.0094 | -0.0069 | 0.0238 | -0.1445 | -0.0185 | -0.0161 | -0.0609 | -0.0587 | -0.0080 | -0.0564 | -0.0755 | -0.0183 | -0.0163 | 0.0449 | -0.0082 | 0.2283 | 0.0590 | 0.4196 | 0.0025 | 0.0488 | 0.0615 | -0.2374 | -0.2673 | 0.0071 | 0.2526 | 0.2245 | -0.0284 | 0.1092 | -0.2611 | -0.1396 | 0.1366 | 0.0287 | -0.0258 | 0.0623 | -0.0213 | 0.0962 | -0.1635 | 0.0518 | 0.0089 | -0.1512 | -0.0188 | -0.0173 | 0.0754 | 0.0321 | 0.0364 | 0.0185 | 0.0079 | 0.0050 | -0.0154 | 0.0148 | 0.1544 | -0.0239 | -0.2445 | -0.0347 | -0.0646 |
| Dimension 22 | 0.0116 | -0.0333 | 0.0196 | 0.0200 | -0.0362 | 0.0545 | -0.0269 | 0.0265 | -0.0482 | -0.0324 | -0.0488 | -0.0446 | 0.0415 | -0.0304 | 0.0225 | -0.1344 | -0.0087 | -0.1337 | -0.0193 | 0.0131 | 0.0057 | -0.0159 | -0.0150 | 0.0153 | 0.0222 | -0.0157 | -0.0027 | -0.1045 | 0.0048 | -0.0801 | -0.0217 | 0.0048 | 0.0249 | -0.0708 | 0.0605 | -0.3035 | 0.1415 | 0.1375 | 0.0015 | -0.0285 | -0.2689 | 0.3940 | -0.1635 | -0.0109 | 0.0929 | -0.0200 | 0.1049 | -0.5728 | 0.0502 | -0.0278 | -0.0009 | 0.0669 | -0.0412 | 0.1245 | -0.1318 | -0.0950 | -0.0678 | -0.0177 | -0.0194 | 0.0620 | 0.0800 | 0.0019 | 0.2627 | -0.0267 | -0.0324 | -0.1217 | 0.1717 |
| Dimension 23 | 0.0113 | -0.0650 | 0.0467 | -0.0114 | 0.0107 | 0.0352 | -0.0073 | 0.0298 | 0.0107 | -0.0531 | -0.1998 | 0.0305 | 0.0408 | -0.0514 | 0.0145 | -0.2149 | -0.0409 | -0.2248 | -0.0572 | -0.0487 | -0.0250 | -0.0668 | -0.0923 | -0.0040 | -0.0110 | -0.0208 | -0.0017 | 0.0105 | -0.0194 | -0.3306 | -0.0220 | 0.0076 | 0.0524 | 0.1166 | 0.4117 | 0.1427 | -0.0083 | 0.0499 | 0.1794 | 0.1351 | -0.1992 | 0.1890 | -0.2529 | 0.1802 | -0.1292 | 0.0413 | -0.1370 | 0.2211 | -0.1003 | 0.1423 | -0.0678 | -0.1492 | 0.0304 | -0.0548 | 0.0270 | 0.0405 | 0.0369 | 0.0624 | 0.0526 | -0.0009 | -0.0100 | 0.0142 | 0.0366 | 0.0007 | -0.0531 | 0.0841 | -0.3380 |
| Dimension 24 | 0.0108 | 0.0697 | -0.0438 | 0.0759 | -0.0398 | -0.0009 | -0.0881 | -0.0224 | 0.0151 | -0.1257 | 0.1036 | -0.4345 | 0.0344 | 0.0798 | -0.0049 | 0.2640 | 0.0400 | 0.3848 | 0.0583 | 0.0162 | 0.0575 | 0.1028 | 0.1385 | -0.0079 | 0.0019 | 0.0967 | -0.0056 | 0.2173 | 0.0090 | -0.0777 | -0.0741 | 0.1463 | 0.1531 | 0.0084 | 0.1281 | -0.0198 | -0.0307 | -0.0559 | -0.3348 | 0.0360 | -0.2115 | 0.1992 | -0.1111 | 0.0488 | 0.0368 | -0.0164 | 0.1052 | 0.0316 | -0.0416 | 0.0371 | 0.1605 | 0.0578 | -0.0200 | 0.0368 | -0.0610 | 0.0015 | 0.0119 | -0.0060 | -0.0051 | 0.0034 | -0.0266 | 0.0663 | -0.1295 | -0.0359 | -0.1257 | 0.0362 | -0.2447 |
| Dimension 25 | 0.0105 | -0.0444 | 0.0018 | -0.0064 | -0.0604 | 0.1299 | -0.0235 | -0.0890 | 0.0898 | -0.0646 | 0.2515 | -0.4304 | 0.0018 | -0.0307 | -0.0038 | -0.2535 | -0.0051 | -0.3509 | -0.0790 | 0.0291 | -0.0732 | -0.1051 | 0.0509 | -0.0335 | -0.0111 | -0.1492 | 0.0009 | -0.4977 | -0.0494 | 0.0488 | -0.0020 | 0.0490 | 0.1592 | 0.0128 | -0.0247 | -0.0195 | 0.0972 | 0.0116 | -0.2675 | 0.0291 | 0.1439 | -0.1482 | 0.0400 | 0.0128 | -0.0474 | -0.0193 | 0.0837 | 0.0133 | -0.0116 | 0.0235 | 0.0136 | -0.0244 | 0.0068 | -0.0020 | 0.0174 | 0.0235 | 0.0411 | 0.0202 | -0.0072 | -0.0335 | -0.0857 | 0.0978 | -0.1178 | -0.0601 | -0.0646 | -0.0004 | -0.0921 |
| Dimension 26 | 0.0096 | -0.0022 | -0.0068 | -0.0354 | 0.0319 | -0.0877 | 0.0902 | -0.0066 | -0.0090 | -0.0383 | -0.2616 | 0.3582 | 0.0135 | -0.0153 | 0.0080 | -0.0619 | 0.0375 | -0.1311 | -0.0081 | 0.0042 | -0.0274 | -0.1004 | 0.0838 | 0.0066 | -0.0346 | -0.0191 | 0.0025 | 0.0682 | 0.0133 | -0.0048 | 0.0754 | -0.1742 | -0.1328 | -0.0071 | 0.0265 | -0.1442 | -0.0050 | -0.1385 | -0.5920 | 0.1008 | -0.0452 | -0.0375 | -0.0462 | 0.0676 | 0.2722 | 0.0387 | 0.1168 | -0.0525 | 0.0811 | 0.0586 | -0.2062 | -0.0177 | -0.0359 | 0.0603 | -0.0376 | 0.0105 | 0.0341 | -0.0237 | -0.0153 | -0.0110 | -0.1304 | 0.0701 | -0.2774 | 0.0375 | -0.0383 | 0.0521 | -0.1147 |
| Dimension 27 | 0.0083 | -0.0499 | 0.0321 | -0.2301 | 0.0614 | 0.0535 | 0.0868 | 0.1319 | 0.3578 | -0.0165 | 0.4209 | 0.3505 | 0.1292 | 0.0236 | -0.0222 | -0.0272 | -0.0438 | 0.3041 | -0.0201 | -0.0249 | -0.0054 | -0.1246 | 0.0172 | 0.0174 | 0.0537 | -0.0566 | -0.0000 | -0.2560 | 0.2440 | -0.0374 | -0.0057 | 0.1624 | -0.0265 | -0.0420 | 0.0553 | -0.0986 | 0.0987 | 0.0334 | -0.0228 | 0.1240 | -0.2103 | -0.0371 | -0.0094 | 0.0901 | 0.1055 | 0.0381 | -0.0928 | 0.0669 | -0.1015 | 0.0808 | 0.0612 | 0.0647 | -0.0412 | 0.0218 | 0.1550 | 0.0040 | -0.0909 | -0.0568 | -0.0374 | 0.0375 | 0.0058 | -0.0624 | 0.0223 | -0.0241 | -0.0165 | -0.0348 | -0.0380 |
| Dimension 28 | 0.0076 | 0.0016 | 0.0018 | -0.0514 | 0.0104 | 0.0315 | -0.0551 | 0.1275 | 0.0637 | -0.0580 | 0.0411 | 0.1152 | 0.0229 | 0.0215 | 0.0020 | -0.0386 | 0.0128 | 0.0899 | 0.0195 | 0.0051 | 0.0135 | -0.0044 | 0.0046 | 0.0208 | 0.0092 | 0.0225 | -0.0035 | -0.0424 | 0.0287 | -0.0056 | -0.0696 | 0.0621 | 0.0173 | -0.0165 | 0.0046 | 0.2663 | 0.0063 | 0.1646 | -0.0388 | -0.0450 | 0.2954 | 0.0203 | -0.0957 | 0.0128 | 0.3026 | 0.0822 | -0.0229 | 0.0031 | -0.0132 | 0.0061 | 0.0635 | 0.0099 | -0.0039 | 0.0142 | -0.5150 | -0.0077 | 0.3716 | 0.2816 | 0.1555 | -0.1041 | -0.0735 | 0.0399 | 0.1713 | 0.0061 | -0.0580 | -0.2568 | -0.0700 |
| Dimension 29 | 0.0075 | 0.0166 | -0.1108 | -0.0093 | 0.0407 | 0.0192 | 0.0291 | 0.0458 | 0.0176 | 0.0236 | 0.1190 | -0.0178 | -0.8627 | -0.0241 | 0.0328 | 0.0620 | -0.0311 | -0.0024 | -0.1077 | 0.0763 | 0.0134 | -0.3051 | -0.0445 | -0.1654 | -0.1608 | 0.0026 | 0.0020 | 0.0661 | 0.0753 | -0.0143 | 0.0116 | 0.0837 | -0.0224 | -0.0008 | 0.0158 | -0.0088 | -0.0054 | 0.0368 | -0.0169 | 0.0164 | -0.0957 | 0.0601 | -0.0296 | -0.0131 | 0.0086 | 0.0030 | -0.0426 | 0.0110 | 0.0061 | 0.0094 | -0.0810 | 0.0228 | -0.0073 | -0.0175 | -0.0239 | 0.0125 | 0.0275 | 0.0357 | 0.0128 | -0.0135 | 0.0011 | 0.0189 | -0.0094 | 0.0306 | 0.0236 | -0.0284 | 0.0315 |
| Dimension 30 | 0.0073 | 0.0737 | -0.0162 | -0.1549 | 0.0125 | 0.0626 | -0.0120 | 0.0279 | 0.1905 | 0.0883 | 0.0987 | -0.1558 | 0.0824 | 0.0815 | -0.0627 | 0.2317 | 0.0485 | -0.0559 | 0.1025 | -0.0171 | -0.0279 | 0.0338 | 0.0294 | -0.0213 | -0.0196 | -0.0084 | 0.0020 | 0.0472 | 0.1464 | 0.0675 | 0.2099 | -0.1861 | -0.1431 | 0.2185 | -0.1643 | 0.3835 | 0.0552 | 0.1417 | -0.0224 | 0.1052 | -0.1382 | 0.0082 | -0.1730 | 0.2391 | -0.1691 | -0.0391 | 0.0747 | -0.2403 | 0.0820 | 0.1202 | -0.3670 | -0.0295 | 0.0655 | -0.0896 | 0.0310 | 0.0256 | 0.0737 | 0.0570 | 0.0211 | -0.0424 | -0.0418 | 0.0494 | -0.0010 | -0.0456 | 0.0883 | 0.0456 | 0.1215 |
| Dimension 31 | 0.0069 | -0.0435 | 0.0019 | 0.0529 | 0.0213 | -0.0443 | 0.0450 | -0.0132 | -0.0914 | -0.0725 | -0.0703 | 0.1920 | -0.0595 | -0.0547 | 0.0439 | -0.1513 | -0.0286 | 0.0667 | -0.0711 | 0.0150 | -0.0011 | -0.0144 | 0.0238 | -0.0259 | 0.0302 | -0.0087 | 0.0004 | -0.0427 | -0.0550 | 0.0239 | -0.1429 | 0.1559 | 0.0874 | 0.0687 | -0.0389 | 0.6161 | -0.0629 | -0.0590 | -0.1516 | -0.0659 | 0.0199 | 0.0360 | 0.0388 | -0.0756 | -0.0296 | -0.0560 | 0.0248 | -0.4268 | -0.0503 | -0.0097 | 0.2228 | 0.0325 | 0.0373 | -0.0603 | 0.3221 | 0.0408 | -0.1178 | -0.0324 | -0.0123 | 0.0252 | 0.0709 | -0.0018 | -0.0422 | 0.0355 | -0.0725 | -0.0877 | -0.1282 |
| Dimension 32 | 0.0065 | 0.0025 | -0.0084 | -0.0140 | 0.0269 | 0.0124 | 0.0233 | -0.0397 | -0.0250 | -0.0144 | -0.0454 | 0.0910 | -0.0496 | -0.0069 | -0.0110 | 0.0164 | 0.0057 | -0.0610 | -0.0372 | -0.0042 | -0.0427 | 0.0750 | -0.0215 | -0.0140 | 0.0023 | -0.0433 | -0.0025 | -0.0072 | -0.1315 | 0.1526 | 0.0045 | 0.0926 | 0.1773 | 0.6612 | -0.3575 | -0.1556 | 0.0258 | 0.0215 | 0.0068 | 0.0803 | -0.0001 | 0.1094 | -0.2393 | 0.1354 | 0.1775 | 0.0709 | -0.1344 | 0.0888 | -0.0248 | 0.0639 | 0.3174 | -0.0342 | 0.0014 | 0.0013 | 0.0079 | -0.0286 | -0.0070 | -0.0409 | 0.0007 | -0.0220 | -0.0430 | -0.0197 | 0.0034 | 0.0345 | -0.0144 | 0.1359 | 0.0913 |
| Dimension 33 | 0.0064 | -0.0989 | 0.0622 | 0.1334 | 0.0363 | -0.0679 | 0.0447 | -0.0593 | -0.3067 | -0.0670 | -0.0053 | -0.0729 | 0.0960 | -0.0842 | 0.0468 | -0.2473 | -0.1038 | 0.2646 | -0.0349 | -0.0168 | 0.0517 | -0.2782 | 0.0973 | 0.0512 | 0.1346 | 0.0386 | 0.0005 | -0.0354 | 0.3079 | 0.0565 | -0.1418 | 0.1887 | -0.2165 | 0.2692 | -0.1524 | -0.0795 | -0.0288 | -0.0242 | -0.0099 | -0.0465 | 0.1177 | 0.0962 | -0.0757 | -0.0343 | -0.1677 | -0.0660 | 0.1490 | 0.0876 | -0.1525 | -0.0322 | -0.3721 | 0.0365 | 0.0263 | -0.0094 | -0.0505 | -0.0019 | 0.0302 | 0.0152 | -0.0081 | -0.0359 | 0.0513 | -0.0283 | 0.0345 | 0.0044 | -0.0670 | 0.0234 | -0.0049 |
| Dimension 34 | 0.0060 | 0.0439 | -0.0368 | -0.0504 | 0.0646 | 0.0018 | 0.1235 | 0.0735 | 0.0731 | -0.0394 | -0.0455 | 0.2345 | -0.0048 | -0.0793 | -0.0553 | 0.2729 | 0.0305 | -0.2560 | -0.0705 | -0.0238 | -0.0218 | 0.2304 | -0.0089 | -0.0992 | -0.1279 | -0.1424 | 0.0010 | 0.0205 | 0.1781 | -0.0042 | -0.2003 | 0.2271 | 0.0198 | 0.0528 | -0.0158 | -0.1302 | 0.0166 | -0.0123 | -0.0653 | -0.0265 | 0.0328 | -0.0050 | -0.0000 | 0.0016 | -0.4082 | -0.1271 | 0.4604 | 0.0844 | 0.0393 | 0.0194 | 0.1165 | 0.0368 | 0.0595 | -0.0274 | -0.0704 | 0.0509 | 0.0853 | -0.0073 | -0.0434 | -0.0631 | 0.0216 | -0.0078 | 0.1215 | -0.0013 | -0.0394 | -0.1601 | -0.1118 |
| Dimension 35 | 0.0059 | 0.0444 | 0.0028 | 0.0688 | 0.0170 | -0.0444 | 0.0495 | 0.0339 | -0.0553 | -0.0620 | -0.0128 | -0.1613 | 0.1199 | -0.0616 | -0.1025 | 0.3205 | 0.0200 | -0.3461 | 0.0181 | -0.0751 | 0.0441 | -0.0026 | 0.0005 | 0.0511 | -0.1817 | -0.1298 | 0.0022 | 0.0551 | 0.3287 | -0.0033 | -0.2182 | 0.2612 | -0.1023 | 0.0381 | -0.0160 | 0.0300 | -0.0158 | -0.0572 | 0.0593 | -0.0270 | 0.0245 | 0.0086 | 0.0585 | -0.0859 | 0.3376 | 0.1023 | -0.3874 | -0.0408 | 0.0231 | -0.0301 | -0.1764 | 0.0353 | -0.0582 | 0.0375 | 0.1245 | -0.0257 | -0.1096 | -0.0286 | 0.0181 | 0.0590 | 0.0151 | -0.0044 | -0.0380 | -0.0270 | -0.0620 | -0.1525 | -0.0778 |
| Dimension 36 | 0.0058 | 0.0204 | -0.0519 | -0.0211 | -0.0345 | 0.0028 | -0.0352 | 0.0130 | 0.1442 | -0.0084 | -0.0253 | -0.0756 | -0.1557 | 0.1318 | 0.1230 | -0.2097 | 0.0681 | 0.1302 | -0.0521 | 0.0994 | -0.0806 | 0.4635 | -0.1139 | -0.0898 | 0.0545 | 0.1008 | -0.0015 | -0.0842 | 0.0249 | 0.0216 | -0.1450 | -0.2787 | -0.0931 | 0.1816 | -0.0738 | -0.0945 | 0.0051 | -0.1050 | 0.0323 | 0.0190 | 0.0107 | 0.0638 | -0.0007 | -0.0883 | 0.0759 | -0.0082 | -0.0204 | 0.0853 | 0.0450 | -0.0112 | -0.2248 | 0.0123 | -0.0364 | 0.0314 | 0.1876 | 0.0100 | -0.0864 | 0.0260 | -0.0043 | 0.0128 | 0.0264 | 0.0189 | 0.0359 | -0.0176 | -0.0084 | -0.4733 | -0.2233 |
| Dimension 37 | 0.0056 | -0.0167 | -0.0392 | 0.0588 | -0.0087 | -0.0933 | -0.1619 | 0.2142 | -0.0354 | -0.0016 | -0.0494 | 0.0132 | -0.1156 | 0.0256 | 0.0928 | -0.1677 | 0.0614 | 0.0012 | -0.1893 | 0.0631 | -0.0931 | 0.5340 | 0.0031 | -0.1054 | 0.0044 | 0.0073 | -0.0002 | -0.1237 | 0.3399 | -0.0196 | 0.0186 | 0.1627 | -0.0375 | -0.1030 | 0.0445 | 0.0764 | 0.0023 | -0.0036 | -0.0444 | -0.0317 | -0.0093 | -0.0114 | -0.0063 | 0.0348 | 0.0580 | -0.0181 | -0.0792 | -0.0314 | -0.0940 | -0.0141 | -0.0340 | -0.0009 | 0.0049 | -0.0204 | -0.1360 | -0.0175 | 0.0237 | -0.0288 | 0.0102 | 0.0056 | 0.0277 | 0.0006 | -0.1057 | -0.0483 | -0.0016 | 0.4858 | 0.1901 |
| Dimension 38 | 0.0051 | 0.0747 | -0.0199 | 0.0308 | -0.1408 | -0.2107 | -0.3653 | 0.4166 | 0.1341 | -0.0203 | 0.0521 | 0.0458 | 0.0110 | 0.1204 | -0.0095 | -0.1951 | 0.2058 | -0.1474 | 0.2686 | 0.0768 | 0.1709 | -0.1871 | 0.1664 | 0.1626 | -0.2702 | 0.2989 | 0.0011 | 0.0112 | 0.0057 | 0.0167 | -0.0784 | 0.0485 | 0.0058 | 0.1055 | -0.0431 | -0.0150 | 0.0101 | -0.1371 | 0.1193 | 0.0170 | 0.0360 | 0.0024 | -0.0066 | -0.0441 | -0.0382 | 0.0281 | 0.1582 | 0.0035 | 0.1274 | 0.0255 | 0.0483 | 0.0056 | 0.0042 | 0.0020 | 0.0478 | 0.0047 | -0.0607 | -0.0332 | -0.0090 | 0.0090 | 0.0086 | 0.0063 | -0.0362 | -0.0782 | -0.0203 | 0.0353 | -0.0337 |
| Dimension 39 | 0.0045 | 0.1193 | -0.0013 | -0.0267 | 0.1483 | -0.0078 | 0.2638 | -0.2473 | -0.0465 | -0.0135 | -0.0372 | 0.0246 | -0.1420 | 0.5293 | -0.1006 | -0.1223 | 0.1109 | -0.0992 | 0.3978 | 0.0184 | -0.1832 | 0.0322 | 0.0219 | 0.1132 | 0.2459 | 0.1748 | 0.0009 | -0.0255 | 0.1314 | -0.0111 | -0.0785 | 0.2394 | -0.0042 | -0.0641 | 0.0342 | -0.0085 | -0.0115 | 0.0532 | -0.0231 | -0.0243 | -0.0104 | -0.0082 | 0.0119 | 0.0272 | -0.0325 | 0.0498 | -0.0288 | -0.0109 | 0.1161 | -0.0100 | 0.0505 | -0.2188 | 0.0090 | -0.0060 | 0.0013 | 0.0110 | 0.0236 | -0.0558 | -0.0131 | -0.0030 | -0.0902 | 0.0013 | 0.0690 | -0.0606 | -0.0135 | 0.0300 | 0.0241 |
| Dimension 40 | 0.0043 | -0.0519 | 0.1019 | 0.0331 | -0.0044 | -0.1348 | -0.2346 | 0.0282 | -0.0311 | -0.0089 | 0.0702 | 0.0157 | -0.0710 | 0.1956 | -0.0609 | 0.0949 | -0.2275 | -0.1205 | 0.1060 | -0.1878 | -0.1186 | -0.0261 | -0.4824 | 0.1365 | 0.2087 | -0.0863 | 0.0006 | 0.0223 | 0.0336 | 0.0058 | 0.0195 | -0.0222 | 0.0144 | 0.0111 | -0.0094 | 0.0456 | 0.0020 | -0.0365 | 0.0603 | 0.0381 | -0.0146 | 0.0160 | -0.0211 | -0.0179 | 0.0818 | 0.2288 | 0.3237 | 0.0119 | -0.2590 | -0.0207 | 0.0129 | 0.2276 | -0.1370 | 0.0269 | 0.0266 | -0.0319 | -0.0182 | 0.0281 | 0.0844 | 0.0506 | 0.1140 | 0.1798 | -0.2135 | 0.0080 | -0.0089 | -0.0133 | 0.0207 |
| Dimension 41 | 0.0040 | 0.0318 | -0.0226 | -0.0171 | 0.0144 | -0.0876 | -0.1672 | -0.0440 | -0.0558 | 0.0664 | -0.1243 | 0.0248 | -0.0082 | 0.1570 | -0.0038 | -0.0595 | 0.0302 | -0.1065 | -0.0256 | -0.0280 | -0.0704 | -0.0207 | 0.3075 | -0.0219 | 0.0390 | -0.0512 | 0.0008 | 0.0030 | 0.0798 | -0.0020 | 0.3533 | 0.1050 | 0.0393 | -0.0019 | -0.0056 | -0.0496 | -0.0350 | 0.0323 | -0.0195 | -0.3581 | -0.1074 | -0.0517 | 0.0503 | 0.3399 | 0.0153 | -0.1906 | -0.0731 | 0.0973 | -0.2135 | -0.0406 | 0.0742 | 0.2696 | 0.0196 | -0.1936 | -0.0126 | -0.1229 | -0.1350 | 0.1612 | -0.0230 | 0.0620 | 0.0714 | -0.0166 | -0.0413 | 0.0516 | 0.0664 | -0.2944 | -0.0393 |
| Dimension 42 | 0.0038 | 0.0291 | -0.0358 | -0.0568 | 0.0562 | -0.0135 | -0.0267 | -0.1055 | -0.0832 | 0.0496 | -0.0598 | 0.0154 | 0.0192 | 0.0181 | -0.0138 | -0.0036 | 0.0638 | -0.0124 | -0.0412 | 0.0400 | 0.0040 | 0.0442 | 0.2166 | -0.0310 | -0.0154 | -0.0227 | 0.0011 | -0.0040 | 0.1080 | -0.0001 | 0.3596 | 0.1583 | 0.0181 | -0.0185 | -0.0005 | 0.0112 | 0.0311 | 0.0127 | 0.0953 | 0.4883 | 0.0526 | 0.0353 | -0.0758 | -0.3446 | -0.0327 | -0.0237 | 0.0785 | 0.0209 | -0.0044 | -0.0612 | 0.0751 | -0.0710 | -0.0748 | 0.2881 | 0.1526 | -0.1658 | 0.0046 | 0.3873 | 0.1021 | 0.0106 | 0.1357 | 0.0341 | -0.1141 | 0.0155 | 0.0496 | -0.0733 | -0.0015 |
| Dimension 43 | 0.0037 | 0.0102 | -0.0585 | -0.0499 | 0.0671 | -0.0386 | -0.0420 | -0.1212 | 0.0063 | 0.0033 | -0.0445 | -0.0316 | -0.0323 | -0.2396 | 0.0144 | 0.0015 | 0.1913 | 0.0998 | -0.1678 | 0.1518 | -0.0382 | 0.0056 | 0.2166 | 0.0875 | 0.1162 | -0.1312 | -0.0011 | -0.0237 | 0.0504 | -0.0039 | 0.0454 | 0.0892 | 0.0002 | -0.0232 | 0.0045 | 0.0455 | 0.0092 | -0.0574 | 0.2654 | -0.1739 | -0.0596 | -0.0238 | 0.0306 | 0.1826 | 0.1026 | 0.4917 | 0.3051 | -0.0014 | 0.1726 | -0.0085 | -0.0113 | -0.2229 | -0.1657 | -0.0171 | 0.0398 | -0.0172 | -0.0464 | -0.1161 | 0.1031 | 0.0799 | -0.1492 | 0.2251 | -0.0364 | 0.0472 | 0.0033 | -0.0567 | -0.0112 |
| Dimension 44 | 0.0036 | -0.0034 | 0.0038 | 0.0069 | 0.0349 | 0.0726 | 0.1116 | -0.0510 | -0.1069 | 0.0075 | 0.1231 | 0.0255 | 0.0608 | -0.2199 | 0.0549 | -0.0800 | -0.0366 | 0.0309 | 0.2021 | 0.0627 | 0.2536 | 0.0902 | -0.4192 | -0.0526 | -0.2190 | 0.2154 | -0.0003 | -0.0204 | 0.0697 | 0.0030 | 0.0757 | 0.0902 | 0.0042 | 0.0022 | -0.0083 | -0.0239 | -0.0181 | 0.0670 | -0.1409 | -0.2591 | -0.0362 | -0.0119 | 0.0348 | 0.2231 | -0.0080 | -0.0217 | 0.0370 | 0.0607 | 0.1504 | -0.0275 | 0.0293 | -0.2130 | -0.0407 | 0.0484 | 0.1186 | -0.2645 | -0.0934 | 0.3692 | 0.0459 | 0.0751 | 0.0373 | 0.1018 | -0.0611 | 0.0179 | 0.0075 | 0.0171 | 0.0330 |
| Dimension 45 | 0.0035 | 0.0062 | -0.0447 | -0.0489 | 0.0826 | 0.1566 | 0.1825 | -0.2086 | 0.0331 | -0.0167 | -0.0563 | 0.0027 | 0.0669 | 0.4045 | 0.0321 | -0.0877 | -0.1403 | 0.0364 | -0.1668 | -0.0160 | 0.1844 | 0.0485 | 0.1681 | 0.0310 | -0.5391 | 0.0284 | 0.0010 | -0.0406 | -0.0665 | -0.0019 | -0.2152 | -0.0998 | -0.0053 | -0.0177 | -0.0020 | 0.0486 | -0.0064 | 0.0469 | 0.0993 | -0.0304 | 0.0004 | 0.0002 | -0.0053 | 0.0705 | 0.0019 | 0.1765 | 0.1200 | 0.0057 | -0.1693 | -0.0092 | -0.0489 | 0.2239 | -0.1371 | 0.0813 | 0.0235 | -0.0466 | 0.0172 | 0.0399 | 0.0870 | 0.0525 | 0.0012 | 0.0317 | -0.0277 | 0.1530 | -0.0167 | 0.1341 | 0.0791 |
| Dimension 46 | 0.0034 | 0.0131 | -0.0275 | -0.0686 | 0.0575 | -0.0244 | -0.0415 | -0.2121 | -0.1566 | 0.0544 | 0.0469 | -0.0195 | 0.0476 | -0.0813 | 0.0734 | -0.1073 | -0.0115 | -0.0013 | 0.0702 | 0.0545 | 0.1872 | 0.1085 | -0.2149 | 0.0308 | -0.2738 | 0.1714 | 0.0001 | -0.0207 | 0.1336 | -0.0010 | 0.4128 | 0.1600 | 0.0178 | -0.0112 | 0.0104 | 0.0013 | -0.0095 | -0.0258 | -0.0134 | 0.1573 | -0.0016 | -0.0269 | -0.0331 | -0.0513 | 0.0217 | 0.0893 | -0.0076 | -0.0610 | -0.1059 | 0.0104 | 0.0430 | 0.0417 | 0.0410 | -0.1290 | -0.1236 | 0.3060 | 0.1061 | -0.4472 | -0.0554 | -0.0541 | -0.0515 | -0.0331 | 0.0156 | 0.0983 | 0.0544 | -0.2095 | -0.0673 |
| Dimension 47 | 0.0032 | 0.0845 | -0.1103 | -0.1401 | 0.0817 | -0.0201 | -0.0294 | -0.2198 | 0.1069 | -0.0100 | -0.0044 | -0.0126 | -0.0570 | -0.3213 | 0.0942 | -0.0244 | 0.3512 | -0.1135 | 0.3018 | 0.1966 | 0.0424 | 0.0328 | -0.0245 | 0.0570 | 0.1332 | 0.0225 | 0.0001 | 0.0499 | -0.0249 | -0.0033 | -0.1508 | -0.0391 | -0.0064 | -0.0332 | 0.0094 | 0.0374 | 0.0223 | -0.0807 | -0.0202 | 0.0162 | -0.0006 | 0.0024 | 0.0086 | 0.0209 | -0.0131 | 0.0113 | -0.0194 | 0.0163 | -0.3998 | 0.0250 | -0.0471 | 0.3512 | 0.0133 | 0.1945 | 0.0928 | -0.0779 | 0.0927 | 0.0623 | 0.0138 | -0.0214 | -0.1591 | -0.0939 | 0.1562 | 0.1303 | -0.0100 | 0.1344 | 0.0398 |
| Dimension 48 | 0.0031 | 0.0284 | 0.0165 | 0.0708 | -0.0244 | -0.2939 | -0.1237 | -0.0916 | 0.0269 | 0.0253 | 0.0218 | -0.0173 | 0.0314 | 0.0460 | 0.0012 | 0.0467 | -0.3202 | 0.0020 | -0.1793 | -0.0831 | -0.1826 | -0.0228 | -0.0422 | -0.0345 | -0.0941 | 0.1452 | 0.0009 | -0.0207 | 0.0467 | -0.0007 | 0.1149 | 0.0294 | 0.0081 | -0.0214 | -0.0002 | 0.0445 | 0.0037 | -0.2586 | -0.0867 | -0.0151 | -0.0125 | -0.0078 | -0.0044 | -0.0102 | -0.0566 | 0.0852 | -0.0211 | 0.0144 | 0.0735 | 0.0354 | 0.0160 | 0.0372 | 0.0758 | 0.1412 | 0.1122 | -0.1486 | -0.0193 | 0.0908 | 0.0108 | -0.0311 | -0.5370 | -0.0520 | 0.4324 | -0.0656 | 0.0253 | 0.0293 | 0.0033 |
| Dimension 49 | 0.0030 | -0.0115 | -0.0133 | -0.0180 | 0.0177 | 0.0433 | 0.0098 | -0.0504 | 0.0267 | -0.0056 | -0.0048 | 0.0095 | 0.0014 | -0.0029 | -0.0019 | -0.0041 | 0.0375 | 0.0034 | 0.0685 | 0.0633 | 0.0851 | 0.0223 | -0.0269 | 0.0116 | 0.0133 | -0.0788 | 0.0008 | 0.0094 | -0.0020 | 0.0028 | -0.0428 | -0.0049 | -0.0041 | 0.0076 | -0.0074 | 0.0258 | 0.0077 | -0.0048 | -0.0551 | 0.1590 | 0.0170 | -0.0013 | -0.0214 | -0.1929 | 0.0084 | 0.0392 | 0.0483 | 0.0249 | -0.0381 | 0.0423 | -0.0170 | 0.0222 | -0.0180 | -0.3970 | -0.2880 | 0.2136 | -0.6747 | 0.2764 | 0.0349 | 0.0574 | -0.1989 | 0.0582 | 0.1180 | 0.0808 | -0.0056 | 0.0631 | 0.0304 |
| Dimension 50 | 0.0029 | 0.1625 | -0.0759 | -0.0990 | 0.1291 | -0.0054 | 0.0595 | -0.0731 | -0.0034 | -0.0146 | 0.0214 | 0.0104 | 0.0800 | -0.2804 | 0.0444 | 0.0663 | -0.1525 | -0.0717 | -0.0443 | -0.0423 | -0.5052 | -0.0543 | 0.1107 | -0.1094 | -0.0757 | 0.5952 | 0.0002 | -0.0417 | -0.0227 | -0.0006 | -0.1159 | -0.0265 | 0.0063 | -0.0016 | 0.0042 | -0.0098 | 0.0117 | 0.1362 | 0.0785 | 0.0372 | 0.0112 | -0.0083 | 0.0073 | 0.0095 | 0.0567 | -0.0006 | 0.0336 | -0.0018 | -0.0382 | -0.0259 | 0.0132 | 0.1026 | -0.0489 | -0.0535 | -0.0720 | 0.1089 | -0.1015 | 0.0185 | 0.0179 | 0.0191 | 0.1507 | 0.1147 | -0.1407 | -0.1257 | -0.0146 | 0.0057 | 0.0094 |
| Dimension 51 | 0.0027 | 0.1015 | -0.1050 | -0.0838 | 0.1451 | -0.1361 | -0.2561 | -0.1171 | 0.1006 | -0.0074 | -0.0737 | 0.0243 | 0.0704 | -0.0041 | 0.1192 | -0.0178 | -0.5189 | -0.0026 | 0.2872 | 0.4067 | 0.0782 | -0.0109 | 0.1058 | -0.2456 | 0.0176 | -0.2297 | 0.0005 | 0.0228 | 0.0205 | -0.0023 | -0.1478 | 0.0109 | 0.0109 | -0.0214 | 0.0051 | -0.0260 | 0.0173 | 0.0829 | 0.0737 | 0.0395 | 0.0066 | -0.0028 | -0.0048 | -0.0263 | 0.0802 | -0.1410 | -0.0187 | 0.0040 | 0.0549 | 0.0160 | -0.0007 | -0.0987 | 0.0750 | -0.0631 | 0.0202 | -0.0625 | 0.0591 | -0.0907 | -0.0707 | -0.0176 | 0.0314 | 0.2230 | -0.0394 | 0.0795 | -0.0074 | 0.0172 | 0.0197 |
| Dimension 52 | 0.0026 | -0.0161 | 0.0022 | -0.0234 | 0.0055 | 0.0515 | -0.0085 | -0.0662 | 0.0233 | -0.0091 | 0.0110 | 0.0068 | 0.0002 | -0.0174 | -0.1009 | -0.0006 | 0.1292 | 0.0136 | -0.0982 | -0.0892 | -0.0166 | 0.0076 | -0.0219 | 0.0633 | -0.0186 | 0.1140 | 0.0001 | -0.0186 | -0.0063 | -0.0028 | -0.0493 | 0.0065 | -0.0070 | -0.0475 | 0.0116 | -0.0282 | -0.0015 | 0.0015 | 0.0081 | 0.1141 | 0.0073 | 0.0321 | -0.0450 | -0.2130 | 0.0680 | 0.0441 | 0.0320 | 0.0036 | -0.0021 | 0.1060 | -0.0255 | 0.0395 | 0.2296 | -0.5330 | 0.0507 | -0.6248 | 0.1542 | -0.1060 | -0.1758 | -0.0230 | 0.0024 | 0.1526 | 0.0029 | 0.1408 | -0.0091 | 0.0081 | -0.0046 |
| Dimension 53 | 0.0025 | -0.0101 | 0.0011 | -0.1156 | 0.0601 | -0.0927 | -0.3141 | -0.2549 | 0.0642 | -0.0185 | -0.0062 | 0.0214 | -0.0179 | 0.0242 | -0.4188 | -0.0349 | 0.1183 | 0.0238 | -0.2236 | -0.1786 | 0.1367 | -0.0041 | -0.0680 | -0.0357 | 0.0772 | 0.1395 | -0.0002 | -0.0361 | 0.0204 | -0.0013 | -0.1427 | 0.0350 | 0.0042 | -0.0159 | 0.0088 | -0.0112 | 0.0141 | 0.0774 | 0.0301 | -0.0161 | -0.0014 | -0.0117 | 0.0225 | 0.0937 | 0.0679 | -0.1227 | -0.0137 | 0.0005 | 0.1559 | -0.0358 | -0.0413 | -0.0331 | 0.2672 | 0.2340 | -0.0079 | 0.2057 | -0.0825 | 0.0795 | -0.1694 | -0.1237 | 0.0708 | 0.1319 | -0.0207 | 0.3776 | -0.0185 | 0.0371 | 0.0121 |
| Dimension 54 | 0.0023 | -0.0305 | 0.0401 | -0.0657 | 0.0090 | 0.0544 | 0.0696 | 0.0385 | -0.0880 | 0.0055 | 0.0168 | -0.0173 | -0.0141 | 0.0541 | 0.3651 | 0.0470 | 0.0100 | 0.0248 | 0.0359 | 0.0079 | -0.1335 | 0.0019 | 0.0131 | 0.1848 | -0.1242 | -0.1238 | -0.0003 | 0.0232 | -0.0063 | 0.0001 | 0.0496 | 0.0045 | -0.0061 | -0.0174 | 0.0054 | -0.0127 | -0.0095 | -0.0111 | 0.0640 | -0.1032 | -0.0024 | 0.0047 | 0.0346 | -0.0214 | 0.1025 | 0.2129 | 0.0614 | -0.0087 | -0.0647 | 0.2031 | 0.0059 | -0.0239 | 0.5676 | 0.1899 | -0.0066 | 0.0786 | -0.1104 | 0.1614 | -0.3717 | -0.2162 | 0.1030 | 0.0848 | -0.0311 | -0.1382 | 0.0055 | 0.0042 | -0.0201 |
| Dimension 55 | 0.0022 | 0.0934 | -0.0653 | -0.0823 | 0.1961 | -0.1437 | 0.1626 | 0.0454 | -0.0936 | -0.0024 | 0.0034 | -0.0103 | -0.0051 | -0.0017 | -0.3271 | -0.0864 | 0.0373 | -0.0070 | -0.1383 | 0.0935 | 0.3064 | 0.0126 | -0.0300 | -0.0696 | 0.0537 | -0.0119 | 0.0010 | 0.0276 | -0.0522 | -0.0030 | -0.0137 | -0.1004 | -0.0059 | -0.0194 | -0.0022 | 0.0165 | -0.0105 | -0.0162 | 0.0533 | 0.0999 | -0.0065 | -0.0224 | -0.0384 | 0.1023 | 0.0662 | -0.0063 | 0.0167 | 0.0111 | -0.1398 | -0.2593 | 0.0437 | 0.1051 | 0.1383 | -0.0163 | 0.0007 | -0.0173 | -0.0323 | -0.0163 | -0.0871 | -0.0600 | -0.0527 | 0.2218 | 0.0269 | -0.6382 | -0.0024 | -0.0118 | -0.0072 |
| Dimension 56 | 0.0021 | 0.0362 | 0.0007 | -0.2956 | 0.2300 | -0.2342 | -0.2266 | -0.2183 | -0.0708 | 0.0116 | 0.0141 | -0.0310 | -0.0133 | 0.0080 | -0.0340 | -0.0185 | 0.0246 | 0.0054 | -0.1525 | 0.0356 | 0.0629 | -0.0021 | -0.0578 | 0.1330 | -0.0312 | -0.0623 | 0.0002 | 0.0151 | -0.0200 | -0.0001 | -0.0819 | -0.0452 | -0.0077 | 0.0198 | 0.0016 | -0.0258 | 0.0004 | 0.1347 | -0.1029 | -0.1303 | 0.0206 | 0.0445 | 0.0728 | -0.1503 | -0.0665 | 0.0594 | -0.0265 | -0.0080 | 0.1043 | 0.4610 | 0.0170 | -0.0347 | -0.1351 | -0.0787 | -0.0320 | -0.0119 | 0.0454 | 0.0771 | 0.0187 | 0.1438 | 0.1345 | -0.3969 | -0.0662 | -0.2941 | 0.0116 | 0.0099 | -0.0092 |
| Dimension 57 | 0.0021 | 0.0914 | -0.1212 | 0.1412 | -0.1201 | 0.1958 | 0.1925 | 0.1934 | 0.0176 | 0.0154 | -0.0606 | -0.0098 | 0.0298 | -0.0084 | -0.4564 | -0.0299 | -0.1697 | -0.0307 | -0.0085 | 0.2674 | 0.0642 | 0.0298 | 0.0241 | -0.1042 | 0.1301 | 0.1399 | -0.0002 | -0.0114 | 0.0163 | 0.0012 | 0.1711 | 0.0159 | -0.0042 | 0.0288 | -0.0029 | -0.0129 | 0.0051 | -0.0729 | 0.0323 | -0.2229 | 0.0017 | 0.0245 | 0.0505 | -0.1987 | 0.0157 | 0.1151 | 0.0243 | -0.0064 | -0.1458 | 0.5141 | -0.0093 | 0.0655 | 0.0245 | 0.1108 | 0.0177 | 0.0487 | -0.0041 | 0.0075 | 0.0106 | -0.0445 | 0.0054 | 0.0457 | -0.0179 | 0.0831 | 0.0154 | 0.0027 | -0.0048 |
| Dimension 58 | 0.0020 | -0.0826 | 0.0755 | -0.1150 | 0.0654 | 0.0025 | -0.0065 | -0.0319 | -0.1063 | -0.0038 | 0.0377 | 0.0404 | -0.0012 | 0.0331 | 0.2025 | -0.0004 | 0.1806 | 0.0227 | 0.0682 | -0.3573 | 0.0774 | -0.0057 | 0.0474 | -0.1964 | -0.0184 | -0.0306 | -0.0003 | 0.0048 | -0.0104 | 0.0023 | 0.0171 | 0.0009 | -0.0093 | 0.0003 | -0.0065 | -0.0214 | -0.0069 | -0.0244 | 0.1097 | -0.1208 | 0.0128 | 0.0388 | 0.0530 | -0.1353 | 0.0663 | -0.3247 | -0.0177 | 0.0094 | -0.0033 | 0.3849 | 0.0161 | 0.0215 | -0.1511 | 0.0774 | 0.0443 | 0.0385 | -0.0104 | -0.1182 | 0.2026 | -0.0923 | -0.1474 | 0.5024 | 0.0528 | -0.1192 | -0.0038 | 0.0360 | 0.0203 |
| Dimension 59 | 0.0018 | 0.0024 | -0.0023 | 0.0883 | -0.0301 | -0.0386 | 0.0598 | -0.0033 | 0.0400 | -0.0014 | 0.0067 | 0.0089 | 0.0014 | -0.0083 | 0.0358 | -0.0105 | 0.0326 | 0.0002 | 0.0237 | -0.0974 | 0.0345 | 0.0014 | 0.0214 | -0.0857 | 0.0186 | 0.0060 | -0.0005 | -0.0035 | 0.0026 | 0.0014 | 0.0242 | 0.0010 | -0.0005 | 0.0513 | -0.0065 | 0.0233 | 0.0060 | -0.0190 | 0.0466 | 0.0150 | 0.0120 | -0.0026 | 0.0041 | -0.0556 | 0.0088 | -0.0098 | 0.0017 | 0.0047 | -0.0140 | 0.0362 | 0.0024 | 0.0228 | -0.0502 | -0.0113 | -0.0242 | 0.1941 | 0.2415 | 0.1534 | -0.4957 | 0.7402 | -0.0879 | 0.1574 | 0.0311 | 0.0073 | -0.0014 | 0.0166 | 0.0157 |
| Dimension 60 | 0.0016 | 0.1726 | -0.0720 | 0.5330 | 0.0365 | -0.3988 | 0.1726 | -0.1577 | 0.3881 | 0.0018 | 0.0275 | 0.0103 | 0.0218 | -0.0613 | 0.1461 | -0.0720 | 0.0466 | -0.0302 | 0.0084 | -0.2353 | 0.1807 | 0.0018 | 0.0355 | -0.1509 | 0.0484 | -0.0129 | -0.0006 | -0.0029 | -0.0065 | -0.0003 | 0.0652 | -0.0169 | -0.0039 | 0.0104 | -0.0009 | -0.0052 | 0.0476 | 0.2892 | -0.0021 | -0.0457 | -0.0187 | -0.0141 | -0.0278 | -0.0786 | -0.0075 | 0.1460 | 0.0182 | 0.0054 | -0.0284 | 0.0697 | -0.0008 | 0.0015 | 0.0526 | -0.0055 | -0.0217 | -0.0042 | -0.0352 | -0.0107 | 0.0368 | -0.1227 | 0.0987 | -0.0594 | -0.0611 | -0.0109 | 0.0018 | -0.0089 | 0.0090 |
Principal Component 1:
Principal Component 2:
Principal Component 3:
You've assessed and cleaned the demographics data, then scaled and transformed them. Now, it's time to see how the data clusters in the principal components space. In this substep, you will apply k-means clustering to the dataset and use the average within-cluster distances from each point to their assigned cluster's centroid to decide on a number of clusters to keep.
.score() method might be useful here, but note that in sklearn, scores tend to be defined so that larger is better. Try applying it to a small, toy dataset, or use an internet search to help your understanding.# Over a number of different cluster counts...
# run k-means clustering on the data and...
# compute the average within-cluster distances.
from sklearn.cluster import KMeans
'''For each k value, we will initialise k-means and use the inertia attribute to
identify the sum of squared distances of samples to the nearest cluster centre.'''
Sum_of_squared_distances = []
K = range(10,25)
for k in K:
km = KMeans(n_clusters=k)
km = km.fit(azdias)
Sum_of_squared_distances.append(km.inertia_)
# Investigate the change in within-cluster distance across number of clusters.
# HINT: Use matplotlib's plot function to visualize this relationship.
plt.plot(K, Sum_of_squared_distances, 'bx-')
plt.xlabel('k')
plt.ylabel('Sum_of_squared_distances')
plt.title('Elbow Method For Optimal k')
plt.show()
# Re-fit the k-means model with the selected number of clusters and obtain
# cluster predictions for the general population demographics data.
km = KMeans(n_clusters=17)
#model_general = km.fit(azdias)
model_general = km.fit(X_pca)
predict_general = model_general.predict(X_pca)
It appears to me that the elbow is roughly between 16-18K. I decided to go with a K of 17 as that seemed like the biggest bend between 16-18.
Now that you have clusters and cluster centers for the general population, it's time to see how the customer data maps on to those clusters. Take care to not confuse this for re-fitting all of the models to the customer data. Instead, you're going to use the fits from the general population to clean, transform, and cluster the customer data. In the last step of the project, you will interpret how the general population fits apply to the customer data.
;) delimited.clean_data() function you created earlier. (You can assume that the customer demographics data has similar meaning behind missing data patterns as the general demographics data.).fit() or .fit_transform() method to re-fit the old objects, nor should you be creating new sklearn objects! Carry the data through the feature scaling, PCA, and clustering steps, obtaining cluster assignments for all of the data in the customer demographics data.# Load in the customer demographics data.
customers = pd.read_csv("Udacity_CUSTOMERS_Subset.csv", sep=';')
# Apply preprocessing, feature transformation, and clustering from the general
# demographics onto the customer data, obtaining cluster predictions for the
# customer demographics data.
customers = clean_data(customers)
(0, '13') (2, '34') (4, '41') (5, '34') (6, '23') (7, '15') (9, '15') (11, '14') (12, '22') (14, '51') (15, '15') (16, '15') (17, '14') (18, '41') (19, '24') (21, '43') (22, '24') (23, '51') (24, '33') (25, '22') (26, '25') (27, '44') (28, '54') (29, '51') (30, '32') (31, '24') (32, '51') (33, '25') (35, '14') (41, '24') (42, '43') (45, '34') (47, '43') (49, '15') (50, '15') (52, '35') (57, '24') (61, '32') (63, '25') (64, '12') (66, '15') (73, '54') (74, '14') (75, '25') (76, '24') (77, '12') (78, '31') (79, '24') (80, '13') (81, '25') (82, '34') (83, '35') (86, '25') (88, '41') (93, '54') (95, '24') (97, '45') (98, '41') (99, '35') (103, '24') (107, '14') (108, '22') (109, '54') (113, '34') (134, '45') (141, '41') (144, '25') (145, '43') (146, '43') (155, '25') (158, '15') (159, '34') (160, '33') (164, '41') (169, '41') (173, '22') (174, '51') (175, '15') (176, '41') (182, '22') (183, '51') (186, '25') (187, '12') (189, '14') (191, '43') (193, '31') (194, '41') (208, '24') (209, 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CAMEO_DEU_2015 CAMEO_INTL_2015 LP_LEBENSPHASE_FEIN LP_LEBENSPHASE_GROB PRAEGENDE_JUGENDJAHRE
customers.head()
| ALTERSKATEGORIE_GROB | ANREDE_KZ | FINANZ_MINIMALIST | FINANZ_SPARER | FINANZ_VORSORGER | FINANZ_ANLEGER | FINANZ_UNAUFFAELLIGER | FINANZ_HAUSBAUER | GREEN_AVANTGARDE | HEALTH_TYP | RETOURTYP_BK_S | SEMIO_SOZ | SEMIO_FAM | SEMIO_REL | SEMIO_MAT | SEMIO_VERT | SEMIO_LUST | SEMIO_ERL | SEMIO_KULT | SEMIO_RAT | SEMIO_KRIT | SEMIO_DOM | SEMIO_KAEM | SEMIO_PFLICHT | SEMIO_TRADV | SOHO_KZ | VERS_TYP | ANZ_PERSONEN | ANZ_TITEL | HH_EINKOMMEN_SCORE | W_KEIT_KIND_HH | WOHNDAUER_2008 | ANZ_HAUSHALTE_AKTIV | ANZ_HH_TITEL | KONSUMNAEHE | MIN_GEBAEUDEJAHR | OST_WEST_KZ | WOHNLAGE | KBA05_ANTG1 | KBA05_ANTG2 | KBA05_ANTG3 | KBA05_ANTG4 | KBA05_GBZ | BALLRAUM | EWDICHTE | INNENSTADT | GEBAEUDETYP_RASTER | KKK | MOBI_REGIO | ONLINE_AFFINITAET | REGIOTYP | KBA13_ANZAHL_PKW | PLZ8_ANTG1 | PLZ8_ANTG2 | PLZ8_ANTG3 | PLZ8_ANTG4 | PLZ8_BAUMAX | PLZ8_HHZ | PLZ8_GBZ | ARBEIT | ORTSGR_KLS9 | RELAT_AB | CAMEO_INTL_2015_ones | CAMEO_INTL_2015_tens | DECADE | MOVEMENT | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 4.0 | 1 | 5 | 1 | 5 | 1 | 2 | 2 | 1 | 1.0 | 5.0 | 6 | 5 | 2 | 6 | 6 | 7 | 3 | 4 | 1 | 3 | 1 | 1 | 2 | 1 | 0.0 | 1.0 | 2.0 | 0.0 | 1.0 | 6.0 | 9.0 | 1.0 | 0.0 | 5.0 | 1992.0 | 1 | 7.0 | 2.0 | 2.0 | 0.0 | 0.0 | 4.0 | 3.0 | 2.0 | 4.0 | 4.0 | 1.0 | 4.0 | 3.0 | 1.0 | 1201.0 | 3.0 | 3.0 | 1.0 | 0.0 | 1.0 | 5.0 | 5.0 | 1.0 | 2.0 | 1.0 | 1 | 3 | 2 | 2 |
| 2 | 4.0 | 2 | 5 | 1 | 5 | 1 | 4 | 4 | 1 | 2.0 | 5.0 | 2 | 2 | 1 | 3 | 3 | 7 | 7 | 1 | 2 | 7 | 5 | 6 | 4 | 1 | 0.0 | 2.0 | 1.0 | 0.0 | 1.0 | 6.0 | 9.0 | 1.0 | 0.0 | 1.0 | 1992.0 | 1 | 2.0 | 2.0 | 2.0 | 0.0 | 0.0 | 3.0 | 7.0 | 4.0 | 1.0 | 3.0 | 3.0 | 3.0 | 1.0 | 7.0 | 433.0 | 2.0 | 3.0 | 3.0 | 1.0 | 3.0 | 3.0 | 2.0 | 3.0 | 5.0 | 3.0 | 3 | 4 | 2 | 2 |
| 4 | 3.0 | 1 | 3 | 1 | 4 | 4 | 5 | 2 | 0 | 3.0 | 5.0 | 4 | 5 | 4 | 6 | 5 | 6 | 4 | 5 | 5 | 3 | 5 | 2 | 5 | 4 | 0.0 | 2.0 | 4.0 | 0.0 | 6.0 | 2.0 | 9.0 | 7.0 | 0.0 | 1.0 | 1992.0 | 1 | 3.0 | 0.0 | 3.0 | 2.0 | 0.0 | 3.0 | 3.0 | 4.0 | 4.0 | 3.0 | 4.0 | 3.0 | 5.0 | 7.0 | 513.0 | 2.0 | 4.0 | 2.0 | 1.0 | 2.0 | 3.0 | 3.0 | 3.0 | 5.0 | 1.0 | 4 | 1 | 4 | 1 |
| 5 | 3.0 | 1 | 5 | 1 | 5 | 1 | 2 | 3 | 1 | 3.0 | 3.0 | 6 | 4 | 4 | 1 | 7 | 6 | 4 | 6 | 2 | 5 | 5 | 3 | 3 | 4 | 0.0 | 2.0 | 2.0 | 0.0 | 1.0 | 6.0 | 9.0 | 1.0 | 0.0 | 2.0 | 1992.0 | 1 | 1.0 | 2.0 | 2.0 | 1.0 | 0.0 | 3.0 | 7.0 | 5.0 | 8.0 | 4.0 | 2.0 | 3.0 | 3.0 | 3.0 | 1167.0 | 2.0 | 3.0 | 2.0 | 1.0 | 1.0 | 5.0 | 5.0 | 3.0 | 7.0 | 5.0 | 3 | 4 | 2 | 2 |
| 6 | 4.0 | 1 | 5 | 1 | 5 | 1 | 1 | 2 | 1 | 2.0 | 5.0 | 4 | 2 | 5 | 1 | 6 | 5 | 3 | 4 | 3 | 3 | 1 | 2 | 2 | 4 | 0.0 | 1.0 | 2.0 | 0.0 | 2.0 | 6.0 | 9.0 | 1.0 | 0.0 | 4.0 | 1992.0 | 1 | 7.0 | 4.0 | 1.0 | 0.0 | 0.0 | 4.0 | 6.0 | 2.0 | 5.0 | 4.0 | 2.0 | 4.0 | 4.0 | 3.0 | 1300.0 | 3.0 | 2.0 | 1.0 | 0.0 | 1.0 | 5.0 | 5.0 | 2.0 | 3.0 | 2.0 | 2 | 3 | 2 | 2 |
#normalization using StandardScaler
customers[customers.columns] = scaler.transform(customers[customers.columns].as_matrix())
#transform the customers data using pca object
customers_pca = pca.transform(customers)
#predict clustering using the kmeans object
predict_customers = km.predict(customers_pca)
At this point, you have clustered data based on demographics of the general population of Germany, and seen how the customer data for a mail-order sales company maps onto those demographic clusters. In this final substep, you will compare the two cluster distributions to see where the strongest customer base for the company is.
Consider the proportion of persons in each cluster for the general population, and the proportions for the customers. If we think the company's customer base to be universal, then the cluster assignment proportions should be fairly similar between the two. If there are only particular segments of the population that are interested in the company's products, then we should see a mismatch from one to the other. If there is a higher proportion of persons in a cluster for the customer data compared to the general population (e.g. 5% of persons are assigned to a cluster for the general population, but 15% of the customer data is closest to that cluster's centroid) then that suggests the people in that cluster to be a target audience for the company. On the other hand, the proportion of the data in a cluster being larger in the general population than the customer data (e.g. only 2% of customers closest to a population centroid that captures 6% of the data) suggests that group of persons to be outside of the target demographics.
Take a look at the following points in this step:
countplot() or barplot() function could be handy..inverse_transform() method of the PCA and StandardScaler objects to transform centroids back to the original data space and interpret the retrieved values directly.# Compare the proportion of data in each cluster for the customer data to the
# proportion of data in each cluster for the general population.
general_prop = []
customers_prop = []
x = [i+1 for i in range(17)]
for i in range(17):
general_prop.append((predict_general == i).sum()/len(predict_general))
customers_prop.append((predict_customers == i).sum()/len(predict_customers))
df_general = pd.DataFrame({'cluster' : x, 'prop_general' : general_prop, 'prop_customers':customers_prop})
df_general.plot(x='cluster', y = ['prop_general', 'prop_customers'], kind='bar', figsize=(9,6))
plt.ylabel('proportion of persons in each cluster')
plt.show()
# What kinds of people are part of a cluster that is overrepresented in the
# customer data compared to the general population?
# What kinds of people are part of a cluster that is underrepresented in the
# customer data compared to the general population?
(Double-click this cell and replace this text with your own text, reporting findings and conclusions from the clustering analysis. Can we describe segments of the population that are relatively popular with the mail-order company, or relatively unpopular with the company?)
Congratulations on making it this far in the project! Before you finish, make sure to check through the entire notebook from top to bottom to make sure that your analysis follows a logical flow and all of your findings are documented in Discussion cells. Once you've checked over all of your work, you should export the notebook as an HTML document to submit for evaluation. You can do this from the menu, navigating to File -> Download as -> HTML (.html). You will submit both that document and this notebook for your project submission.